**Previous months:**

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2013 - 1301(8) - 1302(7) - 1303(7) - 1304(5) - 1305(27) - 1306(6) - 1307(8) - 1308(8) - 1309(7) - 1310(11) - 1311(23) - 1312(4)

2014 - 1401(11) - 1402(9) - 1403(19) - 1404(12)

Any replacements are listed further down

[287] **viXra:1404.0290 [pdf]**
*submitted on 2014-04-16 07:09:56*

**Authors:** Koji Sugiyama

**Comments:** 13 Pages.

This paper constructs the zeta functions of the Riemann hypothesis for the sporadic finite simple groups.
Although many researchers have tried the proof of the Riemann hypothesis, they have not resulted in the success. The proof of this Riemann hypothesis has been an important issue of mathematics. In this paper, we construct zeta functions for the sporadic finite simple groups as preparation proving the Riemann hypothesis.
We define the polynomial ring of a group in order to add groups and to add the members of a group.
The argument of a zeta function is a complex number. We can interpret a complex number as the subgroup of a quaternion. Therefore, we can expand the argument of a zeta function to a quaternion. On the other hand, a complex number is one-dimensional complex general linear group. And the sporadic finite simple groups are high dimensional complex general linear groups. Therefore, we can expand the argument of a zeta function to sporadic finite simple groups.
We define the product of groups the direct product. We interpret the cyclic groups of prime order as prime groups. We construct the natural groups of natural order with products of prime groups. Sporadic finite simple groups become subgroups of natural groups because arbitrary finite groups become subgroups of natural groups. We can express arbitrary finite groups by zeta function of prime groups. And we can express arbitrary noncommutative finite groups by zeta function of sporadic finite simple groups.

**Category:** Mathematical Physics

[286] **viXra:1404.0281 [pdf]**
*submitted on 2014-04-16 07:17:56*

**Authors:** Koji Sugiyama

**Comments:** 41 Pages.

This paper derives the contour integral equation of the zeta function by the inverse Mellin transform.

Many researchers have attempted proof of Riemann hypothesis, but have not been successful. The proof of this Riemann hypothesis has been an important mathematical issue. In this paper, we attempt to derive the contour integral equation from the inverse Mellin transform as preparation proving Riemann hypothesis.

We obtain a generating function of the inverse Mellin-transform. We obtain new generating function by multiplying the generating function with exponents and reversing the sign. We derive the contour integral equation from inverse Z-transform of the generating function.

We derive the summation equation, the asymptotic expansion, Faulhaber’s formula, and Nörlund–Rice integral from the contour integral equation.

**Category:** Mathematical Physics

[285] **viXra:1404.0280 [pdf]**
*submitted on 2014-04-16 08:17:13*

**Authors:** Koji Sugiyama

**Comments:** 16 Pages.

This paper let the sum of all natural numbers by damped oscillation summation method of a new zeta function regularization.
The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converges by the regularization. It diverges. This paper let the sum converge by damped oscillation summation method of the new regularization.
Both the integral representation and the series representation have same value for mathematical consistency. One method to let divergent series converge is Abel summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk). However, the sum of all natural numbers does not converge by the medhod. Therefore it is an important issue to find a new summation method.
We define new "sum of all natural numbers" by damped oscillation summation method. The method let the divergent series converge by multiplying convergence factor exp(-εk)cos(εk). The factor is damped and oscillating very slowly. The tradional sum divers for infinite terms. On the other hand, the new "sum" equals the traditional sum for the finite term. And the "sum" converges -1/12.

**Category:** Mathematical Physics

[284] **viXra:1404.0116 [pdf]**
*submitted on 2014-04-13 19:03:13*

**Authors:** Victor Christianto

**Comments:** 8 Pages. This paper has been submitted to Prespacetime Journal. Comments are welcome

In a recent paper, M. Zubair et al. described a novel approach for fractional space generalization of the differential electromagnetic equations. A new form of vector differential operator Del, and its related differential operators, is formulated in fractional space. Using these modified vector differential operators, the classical Maxwell equations have been worked out for fractal media. In the meantime, there are other papers discussing fractional Maxwell equations. However, so far there is no derivation of Proca equations and Proca-type equations for GEM in fractional space. Therefore in this paper I present for the first time a derivation of GravitoElectroMagnetic (GEM) Proca-type equations in fractional space. Considering that Proca equations may be used to explain some electromagnetic effect in superconductor, then fractional GEM Proca-type equations may be expected to explain some gravitomagnetic effects of superconductor for fractal media. It is our hope, that this paper may stimulate further investigation and experiments in particular with respect to gravitomagnetic effects.

**Category:** Mathematical Physics

[283] **viXra:1404.0104 [pdf]**
*submitted on 2014-04-12 12:24:45*

**Authors:** Michail Zak

**Comments:** 2 Pages.

A new class of dynamical systems that have random solutions with chaotic
probability densities is discovered.

**Category:** Mathematical Physics

[282] **viXra:1404.0088 [pdf]**
*submitted on 2014-04-11 11:47:03*

**Authors:** Solomon I. Khmelnik

**Comments:** 14 Pages. in Russian

An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated after some known experiments. It is shown that the moving molecules of flowing liquid interact like electrical charges. The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forcesbecome equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may be used. // Предлагается объяснение механизма возникновения турбулентных течений, которое основано на максвеллоподобных уравнениях гравитации, уточненных на основе известных экспериментов. Показывается, что движущиеся молекулы текущей жидкости взаимодействуют между собой аналогично движущимся электрическим зарядам. Силы такого взаимодействия могут быть расчитаны и включены в уравнения Навье-Стокса как массовые силы. Уравнения Навье-Стокса, дополненные такими силами, становятся уравнениями гидродинамики для турбулентного течения. При этом для расчета турбулентных течений можно использовать известные методы решения уравнений Навье-Стокса.

**Category:** Mathematical Physics

[281] **viXra:1404.0068 [pdf]**
*submitted on 2014-04-08 18:23:33*

**Authors:** Thierry PERIAT

**Comments:** 14 Pages.

A scenario building a link between a gauge approach and a special feature of one of the Ginsburg-Landau fundamental equation is proposed.

**Category:** Mathematical Physics

[280] **viXra:1404.0059 [pdf]**
*submitted on 2014-04-08 00:13:22*

**Authors:** Sergey Kamenshchikov

**Comments:** 18 Pages.

The basic purpose of this work was to suggest universal quantitative description of ergodic system intermediate bifurcation and obligatory conditions of this transition. Conditions for existence of phase state and first order phase transition were introduced in terms of power balance for system volume unit. Extended Fokker – Planck equation with time dependent diffusion factor was formulated. It turned out that for ergodic system with fixed boundary quantized energy spectrum of stable phase states exists. Obtained results may be applied for prediction of ergodic system behavior. If isolation condition is satisfied, phase spectrum quantization allows selecting proper control parameters for system stabilization. Information about current system coarsened energy allows predicting of future stochastic system behavior on the basis of extended Fokker – Planck model.

**Category:** Mathematical Physics

[279] **viXra:1404.0034 [pdf]**
*submitted on 2014-04-05 00:13:33*

**Authors:** Abel Cavaşi

**Comments:** 3 Pages.

A corollary of the reccurence theorem of the Frenet formulas: the darbuzian of any order depends only on variations of the lancretians of lower order.

**Category:** Mathematical Physics

[278] **viXra:1404.0030 [pdf]**
*submitted on 2014-04-04 07:43:10*

**Authors:** Arm Boris Nima

**Comments:** 9 Pages.

We check that the relation between the angle
and the radius of the movement of an
object following a logarithm
spiral of
p
p
SO(2)
is constant.

**Category:** Mathematical Physics

[277] **viXra:1404.0023 [pdf]**
*submitted on 2014-04-03 09:19:10*

**Authors:** Marcos Georgallides

**Comments:** 13 Pages.

In prior articles , the position of points in Spaces creates Momentum [Λ] which is bounded
in the three constant Energy Layer States k1,2,3 [10] . This rotating energy E = Λ λ is transformed into the Acceleration al and Rotational Ellipsoid , and radiated away ,by loosing angular momentum E = r.m.vr and conserved as momentum E = M.v where emission of linear momentum creates vector v of generalized mass M . When vector v = 0 , this rotating Energy is generalized mass M which is mapped on the perpendicular to Λ plane as velocity v̄r which creates Newton smallest equilibrium accelerations (a f + a p = 0) from Centrifugal (Ff) and Centripetal (Fp) forces . On the infinite points of [PNS] and on the infinite dipole AiBi this acceleration vectors create the Wave motion of the infinite dipole AiBi which dipole are composed of the wavelength λ and the rotating Energy Λ . From this Position , Time enters in equations of motion as the meter of changes only .This rotating Energy is interchanged on dipole A B = (λ , Λ= mv) in the Configuration of co variants λ , m , v̄ as ellipsoid in the two perpendicular fields E = [(/x) + (/dy) + (/z)] . Λ and B = [(/x) + (/dy) + (/z)] xΛ following conservation laws only. Classical theories are confined in Space -Time and Planck-time (which are not assessing the outer reality of Spaces ) , with Time , which is only a meter of changes , and not existing differently . Spaces are composed of infinite points which are related each other with a quantum of Work ( Energy ) .The Norm is the Equation of Total Energy State of Monads equal to → ET = •[(k/ λv) .vE ²] ² + [Λ.vB +ΛxvB ] ² = • [(k/λv) .vE.² ]² + T ² ← which is completely refining Time and leaving only λ Λ = k which indicates a Space Energy Universe . Energy in a Vibrating system is either dissipated into Heat (temperature) which is another type of energy { Energy E as momentum vector Λλ is damped on the perpendicular to Λ plane , as it is like a < Spring-mass System with viscous dumping > , on the basic three co-variants of , Energy E , Lagranges generalized mass M = m , and velocity v̄ with Norm the wavelength λ , and secondly on the rotating Energy Λ= r̄.M.ūr } or radiated away. Newton's laws have a Universal application in all Configuration Systems instead of the referred as the Inertial ones . Even also to the smallest circular motion , ( anywhere that exists momentum ) , exists also Centrifugal and Centripetal forces which create acceleration and the Oscillatory motion . Since also velocity v maybe equal to 0 → c → ∞ then the velocity of light is not the faster in universe . In Black Holes Configuration a new Type of light is needed with a greater velocity than that of light to see what is happening . Light which is a quaternion is travelling either as wave ( photon Λ) either as particle (E =Mv̄= r.m.v̄r ) and in both cases as , a travelling Energy λ.Λ = k interchanged in the two perpendicular forced fields E = . Λ and B = x Λ
( Electromagnetic fields ) following conservation laws . Gauss laws spring from this property.
Oscillatory motion is the simplest case of Energy dissipation of Work embodied in dipole .
In the vibratory system , Energy k = λΛ is Spin of Dipole , dissipated on ⊥ to Λ plane and damped as momentum vector λ.mv̄ . Monad ĀB is the ENTITY and [ A ,B – PA , P B ] is the LAW , so Entities are embodied with the Laws . Entity is quaternion A B , and law |AB| = length of points A,B and imaginary part forces PA , P B . Dipole A B = [ λ , Λ ] in [PNS] are composed of the two elements λ , Λ which are created from points A ,B only where Real part |AB| = λ = wavelength (dipoles ) and from the embodied work , λ Λ , the Imaginary part
W = ∫ P.ds =(r.dP) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , where momentum Λ = p= m.v and Forces
dP = P B –P A are the stationary sources of the Space Energy field . The moving charges is velocity v created from the rotating Energy momentum vector [ Ω = (λ.P) = ± Spin ] which creates the Centrifugal force (Ff) , the equal and opposite to it Centripetal force (Fp) and the acceleration ā mapped (damped ) on the perpendicular to Λ plane as → v E||dP and v B dP. F = q.E + q.v̄ x B = q.[ E + v̄ x B ] is Lorentz force in Electromagnetic crossed fields E and B . Since (dP ± Λ ) the work occurring from momentum p = mv = Λ acting on force dP is zero so when v E =0 , momentum Λ = mv only , is exerting the velocity vector v B to the dipole ,
, λ , and the generalized mass M ( the reaction to the change of velocity v̄ ) which creates the component forces , FE || dP .v and FB dP x v .

**Category:** Mathematical Physics

[276] **viXra:1404.0017 [pdf]**
*submitted on 2014-04-02 22:35:49*

**Authors:** Abel Cavaşi

**Comments:** 3 Pages. Contains an English translation from Romanian

We define the generalized helix of order k, then we make a link with movement on the generalized helix.

**Category:** Mathematical Physics

[275] **viXra:1403.0925 [pdf]**
*submitted on 2014-03-24 12:25:15*

**Authors:** Koji Nagata, Tadao Nakamura

**Comments:** 3 pages

We use the validity of Addition and Multiplication.
We provide an example that the two operations
Addition and Multiplication do not commute with each other.
All analyses are performed in a finite set of natural numbers.

**Category:** Mathematical Physics

[274] **viXra:1403.0286 [pdf]**
*submitted on 2014-03-17 06:04:56*

**Authors:** Arm Boris Nima

**Comments:** Pages.

Did you ever wondered what is the Taylor formula
for an arbitrary chosen basis ? The answer
of this question is the Arm theory
introduced in this article.

**Category:** Mathematical Physics

[273] **viXra:1403.0285 [pdf]**
*submitted on 2014-03-17 06:10:06*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the p-Arm theory which give rise to a new mathematical
object that we call the "p-exponential" which is invariant under
p derivation. We calculate its derivate and we use this new
function to solve dierential equations. Next, we
dene its real and imaginary part which are
the p-cosinus and the p-sinus respectively.

**Category:** Mathematical Physics

[272] **viXra:1403.0284 [pdf]**
*submitted on 2014-03-17 06:11:48*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We introduce the Arm prime factors decomposition
which is the equivalent of the Taylor formula
for decomposition of integers on the basis
of prime numbers. We make the link
between this decomposition and
the p-adic norm known in the
p-adic numbers theory.
To see how it works,
we give examples
of these two
formulas.

**Category:** Mathematical Physics

[271] **viXra:1403.0283 [pdf]**
*submitted on 2014-03-17 06:13:24*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We construct the equivalent of the Taylor
formula in the basis of all roots
fx kgK when K is Z iZ,
Q iQ and C.

**Category:** Mathematical Physics

[270] **viXra:1403.0282 [pdf]**
*submitted on 2014-03-17 06:15:09*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We give the developpment of functions in C[z] C[z
1
] with a scalar product which
involves an integral and a residue calculus. Then we give some examples
of those developpments and nd new 'representations' of the
exponential and the logarithm function . We draw those
representations and we see that there are
similar to their original
representations

**Category:** Mathematical Physics

[269] **viXra:1403.0281 [pdf]**
*submitted on 2014-03-17 06:17:47*

**Authors:** Arm Boris Nima

**Comments:** Pages.

We developp the Arm-Lie group theory which is a theory based
onthe exponential of a changing of matrix variable u(X).
We dene a corresponding u-adjoint action, the
corresponding commutation relations in the
Arm-Lie algebra and the u-Jacobi identity.
Throught the exponentiation, Arm-Lie
algebras become Arm-Lie groups.
We give the example of pp
so(2) and
pp
su(2).

**Category:** Mathematical Physics

[268] **viXra:1403.0280 [pdf]**
*submitted on 2014-03-17 06:19:35*

**Authors:** Arm Boris Nima

**Comments:** 6 Pages.

After diagonalizing the Lorentz Matrix,
we nd the frame where the Dirac
equation is one derivation and
we calculate the 'speed' of
the Schwarschild metric

**Category:** Mathematical Physics

[267] **viXra:1403.0279 [pdf]**
*submitted on 2014-03-17 06:20:51*

**Authors:** Arm Boris Nima

**Comments:** 10 Pages.

We calculate the Poisson-Lie sigma model for every 4-dimensional
Manin triples (function of its structure constant) and we
give the 6-dimensional models for the Manin triples
(sl(2; C) sl(2; C)
; sl(2; C); sl(2; C)
),
(sl(2; C) sl(2; C)
; sl(2; C)
); sl(2; C),
(sl(2; C); su(2; C); sb(2; C)) and
(sl(2; C); sb(2; C); su(2; C))

**Category:** Mathematical Physics

[266] **viXra:1403.0278 [pdf]**
*submitted on 2014-03-17 06:22:13*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We calculate the torsion free spin connection on the quantum group Bq[SU2]
at the fourth root of unity. From this we deduce the covariant derivative
and the Riemann curvature. Next we compute the Dirac operator
of this quantum group and we give numerical
approximations of its eigenvalues.

**Category:** Mathematical Physics

[265] **viXra:1403.0277 [pdf]**
*submitted on 2014-03-17 06:24:03*

**Authors:** Arm Boris Nima

**Comments:** 22 Pages.

We study the noncommutative geometry of the dihedral group D6
using the tools of quantum group theory. We explicit the
torsion free regular spin connection and the
corresponding 'Levi-Civita' connection.
Next, we nd the Riemann curvature
and its Ricci tensor. The main
result is the Dirac operator
of a representation of the
group which we nd the
eigenvalues and the
eigenmodes

**Category:** Mathematical Physics

[264] **viXra:1403.0276 [pdf]**
*submitted on 2014-03-17 06:25:21*

**Authors:** Arm Boris Nima

**Comments:** 16 Pages.

We study the Borel algebra dene by [xa; xb] = 2a;1xb
as a noncommutative manifold R
3
. We calculate its
noncommutative dierential form relations. We deduce
its partial derivative relations and the derivative
of a plane wave. After calculating its de Rham
cohomology, we deduce the wave operator and
its corresponding magnetic solution

**Category:** Mathematical Physics

[263] **viXra:1403.0271 [pdf]**
*submitted on 2014-03-16 10:54:34*

**Authors:** Rami Mehrem

**Comments:** 7 pages including 1 figure

Triangular properties of associated Legendre
functions are derived using the Vectorial Addition Theorem of spherical harmonics

**Category:** Mathematical Physics

[262] **viXra:1403.0064 [pdf]**
*submitted on 2014-03-09 15:13:51*

**Authors:** Giuseppe Rauti

**Comments:** 1 Page.

Navier - Stokes Equations.

**Category:** Mathematical Physics

[261] **viXra:1403.0059 [pdf]**
*submitted on 2014-03-09 10:41:32*

**Authors:** Solomon I. Khmelnik

**Comments:** 108 Pages. Book. The rules Clay Mathematics Institute written as follows: "In the case of … the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction." I suggest my decision of this problem.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence. Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found. We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed. The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. // Формулируется и доказывается вариационный принцип экстремума для вязкой несжимаемой и сжимаемой жидкости, из которого следует, что уравнения Навье-Стокса являются условиями экстремума некоторого функционала. Описывается метод поиска решения этих уравнений, который состоит в движении по градиенту к экстремуму этого функционала. Формулируются условия достижения этого экстремума, которые являются одновременно необходимыми и достаточными условиями существования глобального экстремума этого функционала. Книга дополняется открытыми кодами программам в системе MATLAB – функциями, реализующими расчетный метод, и тестовыми программами.

**Category:** Mathematical Physics

[260] **viXra:1403.0042 [pdf]**
*submitted on 2014-03-06 12:20:55*

**Authors:** Giuseppe Rauti

**Comments:** 1 Page.

Lecture notes in Dynamical Systems and Chaos Theory.

**Category:** Mathematical Physics

[259] **viXra:1403.0038 [pdf]**
*submitted on 2014-03-06 14:30:51*

**Authors:** Giuseppe Rauti

**Comments:** 1 Page.

Lecture notes in Quantum Mechanics and General Relativity. Introduction to the String Theory.

**Category:** Mathematical Physics

[258] **viXra:1403.0004 [pdf]**
*submitted on 2014-03-01 09:50:38*

**Authors:** Gary D. Simpson

**Comments:** 11 Pages.

A possibly novel mathematical structure is presented. The structure is a matrix whose elements are quaternions. The structure is distinct from a tensor.

**Category:** Mathematical Physics

[257] **viXra:1403.0002 [pdf]**
*submitted on 2014-03-01 01:01:17*

**Authors:** Vyacheslav Telnin

**Comments:** 7 Pages.

viXra.org 1402.0167 gives general description of raising vector space W in the power M/L. The
result is the new vector space V. In this paper we take W - the 8 – dimensional generalization of
our 4 – dimensional vector space. Then we raise W in the power 1/3. The result is the 2 –
dimensional vector space V. The metric and algebraic tensors for V are the same as in viXra.org
1402.0176.
After that we take some vector from V and use it for construction of Lagrangian. And for
simplicity we restrict us by only first 4 dimensions of W. Then, from the principle of minimal
action, we get the equations for our vector. And we derive that vector from these equations.
Then we define the tensor and vector of energy – momentum for this Lagrangian. And also we
find the density of spin tensor and (with the help of the algebraic tensor) the density of spin
vector. The numerical cofactor in them is 1/3. So we consider that spin of this vector is 1/3. It
coincides with the power of W for V (vector space we took our vector from).

**Category:** Mathematical Physics

[256] **viXra:1402.0176 [pdf]**
*submitted on 2014-02-28 05:27:31*

**Authors:** Vyacheslav Telnin

**Comments:** 1 Page.

The application of the (1402.0167, 1402.0170 viXra.org) to our 4 – dimensional vector space
W when M = 1, L = 2. Cobasics are chosen so that V has simple algebraic and metric tensors.

**Category:** Mathematical Physics

[255] **viXra:1402.0171 [pdf]**
*submitted on 2014-02-27 06:57:14*

**Authors:** Anamitra Palit

**Comments:** 14 Pages. This paper is of a Composite nature.I have included it in the Mathematical Physics Category

The article seeks to investigate several issues concerning the topics: Relativity, Quantum Mechanics and classical physics. The following issues have been
investigated:1)Relativity suggesting virtual particles 2) Lorentz Transformations
Suggestive of a Bypass route 3)Space getting Curved 4) On Higg’s Mechanism 5)On Tensor Equations of a Composite Nature 6) General Covariance and Tensor
Equations 7) On rocket motion 8) Newton’s Law of Gravitation in the Light of GR

**Category:** Mathematical Physics

[254] **viXra:1402.0170 [pdf]**
*submitted on 2014-02-27 07:00:01*

**Authors:** Vyacheslav Telnin

**Comments:** 2 Pages.

The definition of the algebraic tensor for vector space by using the vector
product of vectors from it’s basis. And application it to the our 4 –
dimensional space.

**Category:** Mathematical Physics

[253] **viXra:1402.0166 [pdf]**
*submitted on 2014-02-26 19:05:56*

**Authors:** Gary D. Simpson

**Comments:** 4 Pages.

The objective of this text is to present a method of using vectors and quaternions to produce Euler's Equation. The method presented uses the cross product of vectors in the j-k plane to produce the isine portion of Euler's Equation. The cosine portion of Euler's Equation is produced by the dot product of the same vectors. The method is then generalized to apply to quaternions.

**Category:** Mathematical Physics

[252] **viXra:1402.0151 [pdf]**
*submitted on 2014-02-22 23:59:56*

**Authors:** William O. Straub

**Comments:** 7 Pages.

In a series of papers written over the period 1944-1948, the great Austrian physicist Erwin Schrödinger presented his ideas on symmetric and non-symmetric affine connections and their possible application to general relativity. Several of these ideas were subsequently presented in his notable 1950 book Space-Time Structure, in which Schrödinger outlined the case for both metric and general connections, symmetric and otherwise. In the following discussion we focus on one particular connection presented by Schrödinger in that book and its relationship with the non-metricity tensor. We also discuss how this connection overcomes a problem that Hermann Weyl experienced with the connection he proposed in his failed 1918 theory of the combined gravitational-electromagnetic field. A simple physical argument is then presented demonstrating that Schrödingers’s formalism accommodates electromagnetism in a more natural way than Weyl’s theory.

**Category:** Mathematical Physics

[251] **viXra:1402.0090 [pdf]**
*submitted on 2014-02-13 19:58:42*

**Authors:** editor Florentin Smarandache

**Comments:** Pages.

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics (instantaneous traveling). In the lights of two consecutive successful CERN experiments with superluminal particles in the Fall of 2011, we believe these two new fields of research should begin developing.
A physical law has a form in Newtonian physics, another form in the Relativity Theory, and different form at Superluminal theory, or at Instantaneous (infinite) speeds –according to the S-Denying Theory spectrum.
First, we extend physical laws and formulas to superluminal traveling and to instantaneous traveling. Afterwards, we should extend existing classical physical theories from subluminal to superluminal and instantaneous traveling.
And lately we need to find a general theory that unites all theories at: law speeds, relativistic speeds, superluminal speeds, and instantaneous speeds –as in the S-Multispace Theory.
The First International Conference on Superluminal Physics as New Fields of Research was hold at the University of New Mexico, Gallup Campus, NM 87301, USA, as an electronic conference on 2-4 July 2012.
There were seven papers selected for this volume by the following authors and coauthors: KAIZHE GUO, CHONGWU GUO, CHEN JIANGUO, DONG JINGFENG, MI HAIJIANG, CHANGWEI HU, YANG SHIJIA, GULI, and FU YUHUA.

**Category:** Mathematical Physics

[250] **viXra:1402.0054 [pdf]**
*submitted on 2014-02-07 23:50:24*

**Authors:** Temur Z. Kalanov

**Comments:** 22 Pages.

Analysis of the foundations of standard trigonometry is proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that the foundations of trigonometry contradict to the principles of system approach and contain formal-logical errors. The principal logical error is that the definitions of trigonometric functions represent quantitative relationships between the different qualities: between qualitative determinacy of angle and qualitative determinacy of rectilinear segments (legs) in rectangular triangle. These relationships do not satisfy the standard definition of mathematical function because there are no mathematical operations that should be carry out on qualitative determinacy of angle to obtain qualitative determinacy of legs. Therefore, the left-hand and right-hand sides of the standard mathematical definitions have no the identical sense. The logical errors determine the essence of trigonometry: standard trigonometry is a false theory.

**Category:** Mathematical Physics

[249] **viXra:1402.0050 [pdf]**
*submitted on 2014-02-07 07:40:17*

**Authors:** J. S. Markovitch

**Comments:** 3 Pages.

A special case of the cubic equation, distinguished by having an unusually economical solution, is shown to relate to both the fine structure constant inverse (approximately 137.036) and the sines squared of the quark and lepton mixing angles.

**Category:** Mathematical Physics

[248] **viXra:1401.0215 [pdf]**
*submitted on 2014-01-29 09:25:00*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 31 Pages.

After the concept of a locally scale-invariant spacetime has been introduced in the companion document, now physical experiments on mathematical entities will be performed to find out implications of that model.
With regard to earlier solutions by others, an unbiased inspection of different gravitational scenarios under local scale-invariance
in comparison with physical reality is undertaken.
This gives five results at once: A suspected locality condition, a promising gravitational ansatz, a static solution for the gravitational potential in the subjective picture together with a possible static cosmic redshift, and a set of candidate terms for governing field equations of physical spacetime.

**Category:** Mathematical Physics

[247] **viXra:1401.0162 [pdf]**
*submitted on 2014-01-24 05:45:27*

**Authors:** V.L.Mironov, S.V.Mironov

**Comments:** 8 pages, 2 tables

We present an alternative type of sixteen-component hypercomplex scalar-vector values "space-time sedenions", generating associative noncommutative space-time Clifford algebra.

**Category:** Mathematical Physics

[246] **viXra:1401.0153 [pdf]**
*submitted on 2014-01-22 16:41:37*

**Authors:** Nicolas Poupart

**Comments:** 7 Pages.

This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale.

**Category:** Mathematical Physics

[245] **viXra:1401.0152 [pdf]**
*submitted on 2014-01-22 16:47:29*

**Authors:** Nicolas Poupart

**Comments:** 7 Pages. Original french version of "An explanation of the entropic nature of the mass using classical physics"

Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale.

**Category:** Mathematical Physics

[244] **viXra:1401.0145 [pdf]**
*submitted on 2014-01-20 16:15:01*

**Authors:** Dan Visser

**Comments:** 5 Pages. I hope Proffessor P. Coles , University Sussex UK, takes notice.

The Universe rotates. We live in a Double Torus Universe. A dark matter torus rotates in a larger time torus of refined time smaller than the Planck-time. The Planck-satellite showed a more detailed picture of the CMB related to Big Bang cosmology. However, I have put that in perspective of a new set of equations that belong to the framework of the Double Torus Theory. That shows my proof for a rotational dark matter Flow by warm and cold areas in the CMB. I also explain why the accelerated space-expansion in the Big Bang cosmology is an illusion.

**Category:** Mathematical Physics

[243] **viXra:1401.0140 [pdf]**
*submitted on 2014-01-20 03:08:23*

**Authors:** Sergey Kamenshchikov

**Comments:** 6 Pages.

In the current paper Fokker Planck model of random walks has been extended to non conservative cases characterized by explicit dependence of diffusion and energy on time. A given generalization allows describing of such non equilibrium processes as Levy flights in a classical differential form without use of fractal PDE. Besides it takes into account mixing properties that are obligatory for a certain class of chaotic systems, such as Kolmogorov K – system. It was shown that an abnormal transport is a consequence of the equilibrium distortion and not stationary diffusion. The particular case of fixed boundaries was considered. According to the received solutions it was shown that a system structure can resist a weak disturbance in the vicinity of the discrete regimes, defined by a system scale and its nonlinear properties. These regimes correspond to the exponential increase of quasi regular structure fluctuations. Only fast disruption of regime is possible for other states of the system. It leads to an immediate transition to the chaos.

**Category:** Mathematical Physics

[242] **viXra:1401.0107 [pdf]**
*submitted on 2014-01-15 09:15:08*

**Authors:** Dan Visser

**Comments:** 9 Pages. I hope the press takes notice!

Fly-By- and GPS-satellites reveal an earth-dark matter-halo is affecting the orbit-velocities of satellites. After analysis by a new set of equations, which describe dark matter, dark matter-force and quantum-gravity combined in a new dark energy force-formula, the new formulations match a percentage whereof satellites feel extra gravity. Also the dark matter-density has been calculated. The analysis confirms dark matter exists as a halo around the earth. Secondly it shows what dark matter really is. It also shows what a dark flow is. The dark matter-features are presented in a Double Torus Cosmology, a new model for the universe, which replaces Big Bang cosmology and enables to understand dark matter better!

**Category:** Mathematical Physics

[241] **viXra:1401.0062 [pdf]**
*submitted on 2014-01-08 10:06:09*

**Authors:** Markos Georgallides

**Comments:** 26 Pages.

Primary Dipole dš = ĀB =[a ± b.i] as complex number, and z̄o =[ s, v̄n.i] = [λ ,±Λ .i ] = [λ , Λ] as
quaternion in [PNS] is the ENTITY with the embodied LAW [A , B - PA , PB ],is composed of the two only elements λ , Λ which are created from points A and B , |AB| = λ = wavelength (dipoles ) and from work W = ∫A-B [ P.ds ] = 0 = (dP.r̄) = r̄xp = I.w = [λ.p] = λ.Λ = k2 , the momentum Λ = p = k2/ λ. and Forces dP = P B –P A) ,which are the sources of Space field . Forces dP parallel to the parallel of Space Anti-Space lines [S]≡ [AS], create a Static force field E in (dP, λ) plane , and Forces dP perpendicular to the parallel of Space Anti-Space lines [S]≡[AS] , create a Static force field B which is perpendicular to E and to ( dP,λ) plane . Motion occurs from the moving charges exerted as velocity v ,created from dipole momentum ± Λ when is mapped in force field B as v E|| dP and v B dP with the generalized mass m (the reaction to the motion) which creates the component forces FE = (λm).E , FB = (λm) .v̄ x B.
Velocity vector v\ (v\ E , v\ B) is in [ v \. B \ ] plane forming an angle θ < 180° to the field B , and total force F= FE + F B = (λm). E + (λm). v̄ x B which combination of the two types result in a helical motion, with the stability demand → E = - (v̄xB) = - (v̄.B) which is the alternative conservation of momentum
[ k 2 = Λ²/2λm ] in the two perpendicular fields E , B and in case (λm) = q then force F = FE + FB = q.E + q.v̄ xB = q.[ E + v̄ x B ] → which is Lorentz force . Since Spin ( vortices) Λ , - Λ , are in inverted
order of rotation and vice-versa , then even function f(Λ) = f(-Λ) and odd function is - f(Λ) = f(-Λ) and their sum f(Λ)+f(-Λ)=0 and so, Mapping (graph) of Even function f(Λ),is always symmetrical about Λ axis or a mirror and of Odd symmetrical about the origin and is the interpretation of the Wave nature of spaces
i.e. The Physical Universe behaves as a simple harmonic oscillator . Conjugating quaternion of the
differential time operator and 3D angular speed vector w̄ with negation truth eo = [- λ,xΛ] = 0 then
( ∂/∂t ,

**Category:** Mathematical Physics

[240] **viXra:1401.0056 [pdf]**
*submitted on 2014-01-07 22:27:20*

**Authors:** Victor Christianto

**Comments:** 4 Pages. This article is not yet submitted to any journal. If you know a paper discussing similar idea, please let send to my email: victorchristianto@gmail.com

Here I describe what I can recall from a seminar held in Moscow State University, December 2008. The lecture was given by Prof. Anosov, and the title is relation between fundamental constants. In essence, he tried to describe fine structure constant from Shannon entropy.
My note book on his lecture was lost since several years ago, so this is a derivation out of my memory on that lecture. I am not aware that until now there is a paper discussing link between fine structure constant and Shannon entropy, so I hope that this short article will stimulate further discussion.

**Category:** Mathematical Physics

[239] **viXra:1401.0017 [pdf]**
*submitted on 2014-01-02 11:07:08*

**Authors:** F. F. Mende

**Comments:** 6 Pages.

Is proposed the new method of investigating the thermophysical and structural characteristics of materials and models, based on the measurement of electrostatic pour on, appearing with the heating or mechanical loads.

**Category:** Mathematical Physics

[238] **viXra:1401.0016 [pdf]**
*submitted on 2014-01-02 11:17:59*

**Authors:** Alexander C. Abad, Emmanuel A. Gonzalez, Roderick Y. Yap, L'ubomir Dorcak

**Comments:** 4 Pages.

In this short note, we present the analog realization of a fractional-order differentiator of order alpha=1/2 in 0.35um CMOS technology.

**Category:** Mathematical Physics

[237] **viXra:1312.0241 [pdf]**
*submitted on 2013-12-31 00:02:28*

**Authors:** Claude Michael Cassano

**Comments:** 2 Pages.

The Fine Structure Constant and Boltzman's Constant may be expressed in terms of a small number of notable irrational numbers and integers.

**Category:** Mathematical Physics

[236] **viXra:1312.0226 [pdf]**
*submitted on 2013-12-28 15:51:23*

**Authors:** Salvish Goomanee

**Comments:** 33 Pages. 4 figures

In this paper, the underlying principles about the theory of relativity are briefly introduced and reviewed. The mathematical prerequisite needed for the understanding of general relativity and of Einstein field equations are discussed. Concepts such as the principle of least action will be included and its explanation using the Lagrange equations will be given. Where possible, the mathematical details and rigorous analysis of the subject has been given in order to ensure a more precise and thorough understanding of the theory of relativity. A brief mathematical analysis of how to derive the Einstein’s field’s equations from the Einstein-Hilbert action and the Schwarzschild solution was also given.

**Category:** Mathematical Physics

[235] **viXra:1312.0152 [pdf]**
*submitted on 2013-12-20 08:10:34*

**Authors:** Putenikhin P.V.

**Comments:** 3 Pages. rus (русский)

The logical relationship of the theorems the Fermat’s and the Pythagorean allow to draw conclusions that multidimensional worlds do not exist.

Путенихин П.В. Логическая взаимосвязь теорем Пифагора и Ферма позволяет сделать вывод о том, что многомерные миры не существуют.

**Category:** Mathematical Physics

[234] **viXra:1311.0196 [pdf]**
*submitted on 2013-11-28 21:19:11*

**Authors:** S.C. Gaudie

**Comments:** 11 pages; mostly font 11; A4 paper; UK English; Freelance scientist.

This answers fundamental questions from Wikipedia about Generations of Matter [**web 1] and related properties.
Why are there three generations of quarks and leptons? Why are the ratios of masses of quarks and leptons as they are?
Also, is the ratio of fundamental force strengths related to the size of the universe and why are the ratios as they are?
This theory defines a “fundamental sub-structure" that is a tetrahedron with the further “sub-structure" of spheres.
The 1, 3, 6 “quantum numbers” ratios in this theory show why the relative masses & radii of quarks and the “large leptons” are their “known values”. The ratios for each of these “fundamental sub-structure", “quantum numbers” are 1, 3 & 6; simple integer values.
Another geometrical possibility, with the same values, is based on the spatial axes.
The big picture could be the arrangement of the “fundamental spheres” along the axes of space.
This theory suggests the “fundamental sub-structure" is behind the relative masses of the quarks& “heavy leptons”. The cube root of the mass was used to calculate a diameter ratio parameter. These ratios are also applied to other basic properties of the universe. This “fundamental sub-structure" has also been applied to the relative strengths of the fundamental forces determining the size of the universe at the time of their creation.
There seems to be a universal “template” for the properties of the universe. The ratio numbers can be thought of as "quantum numbers".
The universe is believed to have gone through creation of forces, inflation stages & must, of necessity, have gone through “phase changes". These could be interconnected.
This “theory” combines the above items into ONE overall “theory”.

**Category:** Mathematical Physics

[233] **viXra:1311.0189 [pdf]**
*submitted on 2013-11-28 10:08:45*

**Authors:** Dan Visser

**Comments:** 5 Pages. I hope the press will take notice, especially E. Verlinde of the UvA-NL

In particular calculations have been made for the detection of extraterrestrial high energy neutrinos. Additional the rest-energy of a neutrino is calculated (equivalent to its rest mass). But both calculations are not standard. The calculations are made from the perspective of a new model for the universe: The Double Torus hypothesis. The alternative calculation shows that the result matches a neutrino-incident in the ICECUBE-project in Antartica for a value of 250 TeV energy. Moreover, an extra calculation is made for the expected neutrino rest-energy by the Standard Model (equivalent for its rest-mass). This shows that time roughly 100 times smaller than the Planck-time can generate a neutrino-rest-energy of 2.2 eV. This delivers evidence for the existence of a sub-quantum-domain of refined time that affects dark vacuum-particles; this is dark matter described in the Double Torus-framework. That generates visible quantum-gravitational particles. Such a calculation could also be performed for an electron or a quark. But that is not (yet) performed in this paper. But one of the conclusions is that the detection of high energy neutrinos could turn out to be additional evidence for the existence of rotational Double Torus Universe.

**Category:** Mathematical Physics

[232] **viXra:1311.0182 [pdf]**
*submitted on 2013-11-27 22:43:06*

**Authors:** Claude Michael Cassano

**Comments:** 16 Pages.

All the fermion masses may be determined from merely two numbers dependent on π , e , and a few rational fractions, and all the fermion charges thereafter.,
In this, now, dimension independent revision; the electron mass and the ratio of the muon mass to the electron mass are shown calculable from simple quadratic functions of π , e , and a few rational fractions. All the remaining masses may be determined from from these constants and their indexes determined by the mass-generalized Maxwell's equations. These calculated masses are all well within current specs as of this publication. In fact, more recent neutrino measurements and estimates have put their values into a rather tight range which the computed values in this update fall within.

**Category:** Mathematical Physics

[231] **viXra:1311.0170 [pdf]**
*submitted on 2013-11-25 14:36:42*

**Authors:** Sergey V. Ershkov

**Comments:** 6 Pages. Helmholtz paradox, constant vortex, incompressible ideal flow

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time.
In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids).
Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian.

**Category:** Mathematical Physics

[230] **viXra:1311.0164 [pdf]**
*submitted on 2013-11-25 03:17:10*

**Authors:** Algirdas Antano Maknickas

**Comments:** 5 Pages.

Using equality of full and covariant time derivatives and partial solutions of Helmholtz equation analytical solution of 1D, 2D and 3D Navier-Stokes equations was obtained

**Category:** Mathematical Physics

[229] **viXra:1311.0152 [pdf]**
*submitted on 2013-11-22 10:14:30*

**Authors:** Dan Visser

**Comments:** 5 Pages. I hope the press wil take notice and will publish about the Double Torus framework.

The title of this article presents evidence-based insight of the manner entropy-gravity might work in detail. Entropy-gravity stands in the picture while simultaneously the Double Torus hypothesis posits the universe can no longer be maintained as the Big Bang cosmology. So from the point of view of the Double Torus hypothesis both hypotheses could be theoretically related. The Double Torus hypothesis is point-particle related, but entropy-gravity used string-mathematics. However, entropy-gravity also used the Holographic Principle. So only the string-mathematics seem to be useful and not an expectable physics model; besides it is limited to Big Bang cosmology. Therefore it might be unexpectedly true that the Universe is Double Torus-shaped with dynamics that carry dark vacuum-particles with the same dynamics, namely: A Double Torus sub-quantum generated quantum-gravity whereof optical reality is a part of.

**Category:** Mathematical Physics

[228] **viXra:1311.0133 [pdf]**
*submitted on 2013-11-18 20:20:23*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 4 Pages.

We suggest a new approach to Deformed Special Relativity (DSR) in which we maintain that the Principle of Invariancy of Speed of Light (PISL) must be modified at Planck Scale (PS) but also the Principle of Relativity (PR). We derived a more generalized deformation of Special Theory of Relativity (STR) compare to other DSR theories in a sense that one can show that at a "low--energy approximation", Quantum Mechanics in its simplest form can be derived. This was done by an introduction of a new dimensionless parameter.

**Category:** Mathematical Physics

[227] **viXra:1311.0121 [pdf]**
*submitted on 2013-11-17 06:39:16*

**Authors:** Dan Visser

**Comments:** 13 Pages. I hope the press will take notice of the Double Torus hypothesis and in particular this paper.

Einstein’s energy is connected to a new dark energy force, refined-time, the fundamental constants of Planck and Newton and prove the universe is a rotational Double Torus Universe. Also is proven that an accelerated space-expansion in a stand-alone Big Bang cosmology is an optical illusion. This paper presents a new energy-equation connecting Einstein’s relativistic-energy to a new dark matter-force in a new dark energy force. This new equation is the result of combining a rather new energy-formula of E. Verlinde (UvA-NL) with my new dark energy force-formula of my Double Torus hypothesis. The Double Torus hypothesis is a new model for the universe and against Big Bang Cosmology. A second new equation proves indeed the accelerated space-time expansion is an optical illusion. The new dark energy force uses refined time, which is smaller than the Planck-time. Such causes a cyclic refined time-process from a sub-quantum scale recalculating dark matter towards the quantum scale, but in a rotational Double Torus Universe. This has consequences for the philosophy of past and future.

**Category:** Mathematical Physics

[226] **viXra:1311.0109 [pdf]**
*submitted on 2013-11-15 21:30:44*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 4 Pages.

We suggest a generalized deformation on Lorentz Invariance at the Planck Scale based on the work of Maguiejo and Smolin [3] on Doubly Special Relativity (DSR) theories. The result from Maguiejo-Smolin dispersion relation of having a varying Planck's "constant" and the Planck Energy that is perfectly classical at Planck Scale was also generalized by introduction of a dimensionless parameter.

**Category:** Mathematical Physics

[225] **viXra:1311.0108 [pdf]**
*submitted on 2013-11-16 01:26:45*

**Authors:** Vyacheslav Telnin

**Comments:** 8 Pages.

At first the 4-dimensional real basis spinors are set in accordance to usual 2-dimensional complex basis spinors. This is the first step. Then the 4-dimensional space of real basis spinors represents as the tensor product of two 2-demensional spaces. Further the sum of these two 2-dimensional spaces represents as the tensor product of two new 2-dimensional spaces. And this operation repeats infinitely.The metric tensor defines for each of derived in this process spaces (as for 2-
dimensional, so for 4-dimensional). The shortage of data at this process compensates by the simplicity principle.

**Category:** Mathematical Physics

[224] **viXra:1311.0106 [pdf]**
*submitted on 2013-11-15 15:08:38*

**Authors:** M. D. Sheppeard

**Comments:** 10 Pages.

A simplicial category is associated to topological structure for generic classical spaces. It may be augmented by algebraic structure using noncommutative monomials. For instance, the tetrahedral numbers n(n+1)(n+2)/6 hide 4^(n-1) paths on a lattice. This paper is a basic introduction to these numbers, with a view to recovering ordinary simplices only beyond infinite n. The simplex diagrams hint at fractals in the sense that a point on an edge hides a copy of the edge.

**Category:** Mathematical Physics

[223] **viXra:1311.0102 [pdf]**
*submitted on 2013-11-14 23:00:00*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 7 Pages.

The Wave Metric Theory (WMT), recently introduced by this author in [4], was discussed here in a more direct and simple way as an introduction to many who had never heard this approach to Unification Problem.

**Category:** Mathematical Physics

[222] **viXra:1311.0099 [pdf]**
*submitted on 2013-11-14 12:53:12*

**Authors:** M.E. Hassani

**Comments:** 30 Pages; 45 References

The paper provides a crucial elementary derivation of new superluminal spatio-temporal transformations based on the idea that, conceptually and kinematically, each subluminal, luminal and/or superluminal inertial reference frame has,in addition to its relative velocity, its proper specific kinematical parameter,which having the physical dimensions of a constant speed. Consequently,the relativity principle and causality principle are coherently extended to superluminal velocities and, more importantly, this original approach constitutes the first basic step toward the formulation of superluminal relativistic mechanics in which the standard special relativity theory should be a particular case.

**Category:** Mathematical Physics

[221] **viXra:1311.0090 [pdf]**
*submitted on 2013-11-12 04:08:29*

**Authors:** Vyacheslav Telnin

**Comments:** 5 Pages.

From the fact, that 2-dimensional basis spinors are complex, there are made two conclusions. The first is that it is possible to change them by
4-dimensional real basis spinors. The second is that it is possible to enter 12 more dimensions in addition to 4 ordinary dimensions of our space.
There is found connection of the basis of that 16-dimensional space with the basis of 4-dimensional space of real basis spinors.

**Category:** Mathematical Physics

[220] **viXra:1311.0085 [pdf]**
*submitted on 2013-11-11 19:43:14*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 3 Pages. In Commemoration of the 11th Year Anniversary of Perelman's Posting of His First Paper on the use of Ricci Flow to Solve Poincare's Conjencture.

We further elaborated the Wave Metric Theory as a unification theory by giving emphasis on one of its assertions: the "Hierarchy of Metrics" that exists in Nature . We showed that there are three levels in the hierarchy and all can be described by a unified evolution equation.

**Category:** Mathematical Physics

[219] **viXra:1311.0082 [pdf]**
*submitted on 2013-11-12 01:05:58*

**Authors:** John Frederick Sweeney

**Comments:** 13 Pages. 1 photo, 3 charts in Chinese

With a horary chart from the time the author learned of the news of ABC news woman Amy Robach’s (Good Morning America) announced double mastectomy, this paper provides a prognosis for Robach’s chances of survival via medical divination under Qi Men Dun Jia, an ancient Egytian form of divination. Since the sign of a scientific model and theory is to predict, the accurate prediction included herein will suffice to prove the accuracy and scientific validity of Qi Men Dun Jia.

**Category:** Mathematical Physics

[218] **viXra:1311.0057 [pdf]**
*submitted on 2013-11-08 22:55:36*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 6 Pages. In Commemoration of the Centennial Anniversary of the Publication of Nordstrom Theory

We further elaborated the Wave Metric Theory as a unification theory by giving emphasis on being a metric theory and showing that its precursor is the first metric theory put forward by Nordstrom a hundred years ago.

**Category:** Mathematical Physics

[217] **viXra:1311.0054 [pdf]**
*submitted on 2013-11-07 23:06:56*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 5 Pages.

We presented a short summary on how the Wave Metric Theory (WMT), recently introduced by this author, can also be used as a basis for cosmological models. A comparison was made with other unpopular cosmological models that had been put forward recently. The link from cosmology to interpretational problem of quantum mechanics was also discussed. A general overview of what to consider in setting up a cosmological model was discussed based on WMT.

**Category:** Mathematical Physics

[216] **viXra:1311.0049 [pdf]**
*submitted on 2013-11-06 23:15:21*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 10 Pages.

We presented a metric theory which we called as the Wave Metric Theory (WMT) based on the recent work of this author [1],[2],[3] that applies at Quantum Level (QL) down to the subquantum level (SQL) at the Planck Scale (PS). It considers curvature (the gravitational field) might arise as a kind of "averaging" over very complicated topological phenomena at very small scales, the so-called "spacetime foam" as suggested since the time of Wheeler. It is shown that the metric is conformally covariant, Nordstrom in nature and its transformation follows a Hyperbolic type of Ricci Flow. We then show that Einstein's Theory of Relativity (ETR) and conventional Quantum Mechanics (QM) can be derived from it as a "low-energy approximation".

**Category:** Mathematical Physics

[215] **viXra:1311.0045 [pdf]**
*submitted on 2013-11-06 08:00:28*

**Authors:** Dmitri Martila

**Comments:** 2 Pages.

Mustiness basement of Science were blown up, in time of rising Einstein. He has not taken any of the Newtonian principles (three dimensional World with absolute time) into General Relativity. The beam of starlight passing in Sun's low gravity, showed, that even in weak field limit the General Relativity empirically contradicts the Newton's theory. Nowadays the Science is slow. I propose to critically examine its foundations once again. Because there are experiences, which contradict the Science. And the entropy, as it not being sold on market, is mystical enough.

**Category:** Mathematical Physics

[214] **viXra:1311.0025 [pdf]**
*submitted on 2013-11-04 09:17:55*

**Authors:** Solomon I. Khmelnik

**Comments:** 14 Pages.

An explanation is offered of the mechanism of turbulent flows emergence, based of the Maxwell-like gravitation equations, updated after some known experiments. It is shown that the moving molecules of flowing liquid interact like electrical charges.
The forces of such interaction can be calculated and included to the Navier-Stokes equations as mass forces. Navier-Stocks equations complemented by these forcesbecome equations of hydrodynamics for turbulent flow. For the calculations of turbulent flows the known methods of Navier-Stokes equations solution may be used.

**Category:** Mathematical Physics

[213] **viXra:1311.0011 [pdf]**
*submitted on 2013-11-02 07:17:21*

**Authors:** Thierry PERIAT

**Comments:** 11 Pages.

The motivations for introducing a “new” mathematical tool within the general theory of relativity (A. Einstein’s work - GTR) have been intensively exposed in a first paper [vixra.org; 1311.0004]. This “companion” paper develops an argumentation allowing the intervening of the same tool in a pure 4D space. So far we know, it is one of the first theoretical works connecting the GTR and the Quantum Theory in a plausible manner at the Planckian limit.

**Category:** Mathematical Physics

[212] **viXra:1311.0004 [pdf]**
*submitted on 2013-11-01 12:11:05*

**Authors:** Thierry PERIAT

**Comments:** 18 Pages.

This article is the first part of a research connecting the A. Einstein's general relativity and the Quantum Theory. The connection is realized via the canonical 3 + 1 ADM procedure and the introduction of a mathematical tool which is nothing but just a kind of inner product.

**Category:** Mathematical Physics

[211] **viXra:1310.0235 [pdf]**
*submitted on 2013-10-26 10:57:34*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 20 Pages.

A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor.
The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined.

**Category:** Mathematical Physics

[210] **viXra:1310.0234 [pdf]**
*submitted on 2013-10-26 11:40:40*

**Authors:** Solomon I. Khmelnik

**Comments:** Pages. The rules Clay Mathematics Institute written as follows: "In the case of … the Navier-Stokes problem, the SAB will consider the award of the Millennium Prize for deciding the question in either direction." I suggest my decision of this problem.

In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional. We describe the method of seeking solution for these equations, which consists in moving along the gradient to this functional extremum. We formulate the conditions of reaching this extremum, which are at the same time necessary and sufficient conditions of this functional global extremum existence.
Then we consider the so-called closed systems. We prove that for them the necessary and sufficient conditions of global extremum for the named functional always exist. Accordingly, the search for global extremum is always successful, and so the unique solution of Naviet-Stokes is found.
We contend that the systems described by Navier-Stokes equations with determined boundary solutions (pressure or speed) on all the boundaries, are closed systems. We show that such type of systems include systems bounded by impermeable walls, by free space under a known pressure, by movable walls under known pressure, by the so-called generating surfaces, through which the fluid flow passes with a known speed.
The book is supplemented by open code programs in the MATLAB system – functions realizing the calculation method and test programs. Links on test programs are given in the text of the book when the examples are described. The programs may be obtained from the author by request at solik@netvision.net.il

**Category:** Mathematical Physics

[209] **viXra:1310.0232 [pdf]**
*submitted on 2013-10-25 21:23:26*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 13 Pages.

We attempt to generalized the Lorentz Transformation using the Implex Number System recently introduced by this author as an alternative approach on modifying the Lorentz Invariance at the Planck Scale different from the approach of "Doubly Special Relativity" (DSR) theories. Instead of just the Principle of Invariancy of Speed of Light (PSL) was violated in a sense that other fundamental quantities (e.g. Planck energy/mass) is ought to be invariant, we take into consideration that all known "Laws of Physics" are violated. The word "all" constitutes not only the two postulates of Special Theory of Relativity (STR) but also the postulate of Quantum Mechanics specifically the Heisenberg Uncertainty Principle (HUP). It is shown that the metric of the spacetime at the Planck Scale is oscillating and conformally invariant. A generalized evolution equation of the metric was derived base on the recent work on Ricci flow as a mathematical description of the "quantum foam".

**Category:** Mathematical Physics

[208] **viXra:1310.0231 [pdf]**
*submitted on 2013-10-25 21:29:54*

**Authors:** Jian-zhong Zhao

**Comments:** 17 Pages.

Mathematical provability , then classification, of Saint-Venant's Principle are discussed. Beginning with the simplest case of Saint-Venant's Principle, four problems of elasticity are discussed mathematically. It is concluded that there exist two categories of elastic problems concerning Saint-Venant's Principle: Experimental Problems, whose Saint-Venant's Principle is established in virtue of supporting experiment, and Analytical Problems, whose Saint-Venant's decay is proved or disproved mathematically, based on fundamental equations of linear elasticity. The boundary-value problems whose stress boundary condition consists of Dirac measure, a "singular distribution ", can not be dealt with by the mathematics of elasticity for " proof " or "disproof " of their Saint-Venant's decay, in
terms of mathematical coverage.

**Category:** Mathematical Physics

[207] **viXra:1310.0191 [pdf]**
*submitted on 2013-10-22 11:40:05*

**Authors:** Malcolm Macleod

**Comments:** 1 Page.

In this essay I propose an expanding black-hole universe (ours) with a contracting white-hole universe twin. Units of Planck momentum are transferred discretely from the white-hole to the black-hole thereby giving a rationale for the expansion of the universe, time, the arrow of time, dark energy and dark matter.

**Category:** Mathematical Physics

[206] **viXra:1310.0165 [pdf]**
*submitted on 2013-10-17 04:11:02*

**Authors:** Claude Michael Cassano

**Comments:** 17 Pages.

A soliton solution of the Klein-Gordon equation, ke^{-|m⋅r|} , consistent with the mass-generalized Maxwell's equations and the preon foundation for the fermions is presented, proved and discussed.

**Category:** Mathematical Physics

[205] **viXra:1310.0146 [pdf]**
*submitted on 2013-10-16 11:16:19*

**Authors:** Marcos Georgallides

**Comments:** 15 Pages.

Lagrange equation of motion for a single point ( Primary Point A is the only Space ) , states that this point must move from the Initial Position A to another position say B . This Equilibrium for points A and B , presupposes in Mechanics the Principle of Virtual Displacements and the work done is W = ∫ P.ds = 0 , or when ds = distance AB then →
[ ds .( PA + P B ) = 0 ] ...(1).. From Equation (1) are self created all the Spaces [S] the equilibrium Anti-Spaces [AS] and the Sub-Spaces [SS] with infinite points in them and with a finite work on it . Monad dš (dipole AB) is a complex number of type [ dš = z = x+i.y ] ..(1a) representing the real part (x) , the distance AB , and imaginary parts (i.y) which is the work of …(1) . Complex number , z , the first dimentional unit AB , is such that either repeated by itself as monad ( z• = z.z.z.z. w-times ) or repeated times itself in monad ( ⁿ√z = z /ⁿ = z• , z/ⁿ.z/ⁿ.z/ⁿ….w = 1/n-times , or the nth roots of z equal to w = 1/n ) remains unaltered forming Spaces ( z•) , Anti-spaces( - z•) and the inversing Sub-spaces (ⁿ•z) , meaning that , unit circle is mapped on itself simultaneously on the two bases , 1 and n=1/w , where w.n = 1. This duality of coexistance on AB [ the w.th power and the n.th root of z where w.n =1 ] presupposes a common base ,m, which creates this unit polynomial exponentiation . Analysing this exponentiation according to one of the four basic properties of logs then becomes →
log.w(1= w.n) = log.w(w)+log.w(n=1/w) = 1+1/w = 1+ n
and it is the base of natural logarithms e and since 1= w.n
then → ( 1+ n )• = (1+1/w)• = constant = m = e ← ....(2) Since the first dimentional unit AB is a complex number with many imaginary parts (and this because of the infinite variables) then this unit has the general type of quaternion .i.e.
m^±(ª+₫.i) = q• = (Tq)•.[cos.wφ + ε.sin.wφ] ……where
m = lim(1+1/w)• for w = 1→ ∞ , q = z = ± ( x+y.i )
sinφ = y/•x²+y² , cosφ = x/•x²+y² , |z| = •x²+y²,
Tq = • x²+y1²+y2²+ ….yn² , Ty = • y1²+y2²+ ….yn²
ε = (y.i/Ty)=[y.i ] / [Ty]=(y1.a1+y2.a2+.)/(• y1²+y2²+yn²)
[PNS] ↔ quaternion ↔ [ dŝ = x+i.y ] is a Vector with two components , the one x is the only Space with Scalar Potential field Φo , which is only half lengths of Space , Anti-Space , ( the longitudinal position ) , (x) → (-x) straight line connecting Space [S] , Anti-Space [AS] in [PNS] and in it exist , the initial Work , or Impulse , bounded on points which cannot be created or destroyed which is analogous to the (x) magnitude , and the other one y is the infinite local curl fields So , due to the Spin which is the intrinsic rotation of the Space and Anti-Space . Because in [S] and [AS] forces PA - PB are acting in the same straight line so moment lever is zero ( 0 ) , therefore Primary [S] and [AS] are ir-rotational and so it is possible to express this Primary field as a scalar function (Φo). This shows that [PNS] is a Space Work or Space- Spin or < Space Energy Existence > , where Time is not existing , because Φo and So are not time-varying . The same is holding also for the infinite dipole AiBi which are also complex numbers with all their properties , that of quaternions .
Because quaternion properties are wrapped in lower and higher dimensions only by rotation , this is the property of spaces , so all dipole AnBn may have commons , which may bleed off in any Space , a very useful device for Quantum-mechanics . Geometrically states that , this property of commons allows to the dipole AnBn or to Spaces ↔ [ dŝ = xn+i.yn ] , to be also a Space -Time existence wrapped in the , Space-Energy Existence because of ,
Operation ↔ Quaternion → Notation m^±(ª+₫.i) = q• → = (Tq)•. [cos.wφ + ε.sin.wφ]
Scatters , Part or all Content of the quaternion q , in all Spaces and Sub-Spaces as q•
[ i.e. The duality of coexistence ↔ of the content of dŝ , from w.th power to the n.th root of q , where w.n =1 , is the measuring of , drag areas and other trapped accumulator , and by rotation to convert them in Spaces ]. An extend analysis of this unification follows in [23]

**Category:** Mathematical Physics

[204] **viXra:1310.0082 [pdf]**
*submitted on 2013-10-13 07:52:44*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here.
The equation of momentum has been split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one.
The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity (potential of which should be a harmonic function).
¬¬¬Then we consider equation for solenoidal (divergence-free) field of flow velocity in the proper rotating co-ordinate system. Such a transition transforms the equation of motion to the Helmholtz vector differential equation.
The inverse transformation from the rotating system to ordinary Cartesian coordinate system is possible only in case of constant angular velocity of rotation of such a system.
The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.

**Category:** Mathematical Physics

[203] **viXra:1310.0081 [pdf]**
*submitted on 2013-10-12 16:06:14*

**Authors:** Ali R. Hadjesfandiari

**Comments:** 39 Pages.

By examining the theory of relativity, as originally proposed by Lorentz and Poincaré, the fundamental relationship between space-time and matter is discovered, thus completing the theory of relativity and electrodynamics. As a result, the four-dimensional theory of general motion and the four-dimensional vortex theory of interaction are developed. It is seen that the electromagnetic four-vector potential and strength fields are the four-dimensional velocity and vorticity fields, respectively. Furthermore, the four-vector electric current density is proportional to the four-dimensional mean curvature of the four-vector potential field. This is the fundamental geometrical theory of electromagnetism, which determines the origin of electromagnetic interaction and clarifies some of the existing ambiguities. Interestingly, the governing geometry of motion and interaction is non-Euclidean.

**Category:** Mathematical Physics

[202] **viXra:1310.0021 [pdf]**
*submitted on 2013-10-03 14:27:31*

**Authors:** Thomas Günther

**Comments:** 3 Pages.

This article presents a new exact solution of Einstein’s equations with cosmological constant,
which includes de Sitter’s metric as a special case. The generalized solution admits a nonzero stress energy
momentum tensor. The second section is concerned with a transformation of the line element into a spherical
symmetric but anisotropic form.

**Category:** Mathematical Physics

[201] **viXra:1309.0212 [pdf]**
*submitted on 2013-09-30 16:38:40*

**Authors:** Jeremy Dunning-Davies

**Comments:** 4 Pages. Again it is hoped this short note will provoke more examination of this topic.

Here two derivations of Hamilton’s equations of motion are examined and found to depend crucially on both the system being conservative and the mass being constant. It is speculated that these derivations might be extended to the case where, as well as the system being conservative, the mass varies purely with time. However, at this stage, other generalisations seem unlikely and, if that is so, the usefulness of the Hamilton approach in mechanics would appear to be limited.

**Category:** Mathematical Physics

[200] **viXra:1309.0210 [pdf]**
*submitted on 2013-09-30 14:46:09*

**Authors:** Jeremy Dunning-Davies

**Comments:** 6 Pages. It is hoped this short note will provoke further examination of the topic discussed.

In most, if not all, introductions to classical mechanics, the mass is assumed to be constant. Usually this is mentioned and often attention is drawn to such systems as rocket motion to indicate that, in practice, the mass is not always a constant. In truth, many students actually meet a varying mass for the first time when introduced to the Special Theory of Relativity. However, varying masses do occur in nature when relativistic effects are not important. Here an attempt is made to draw together some common results of classical mechanics with a variable mass taken into account. Particular attention will be drawn to a perceived change in the expression for the kinetic energy and to crucial changes in the basic form of Lagrange’s equations of motion.

**Category:** Mathematical Physics

[199] **viXra:1309.0141 [pdf]**
*submitted on 2013-09-19 10:13:47*

**Authors:** John Frederick Sweeney

**Comments:** 37 Pages. De – Constructing De Marrais Series

The late Robert Marrais wrote of 3 distinct aspects of Sedenion Space: one belonging to the E8 x E8 Super – Symmetry of the embattled Super String Theory, one belonging to Icosahedral Rotation Groups or H3, and a third belonging to O. V. Lyashko. In addition, this paper discusses methods to classify and to categorize the Sedenions.

**Category:** Mathematical Physics

[198] **viXra:1309.0116 [pdf]**
*submitted on 2013-09-17 10:54:11*

**Authors:** John Frederick Sweeney

**Comments:** 34 Pages.

This paper examines a point of intersection between the work of the late Robert de Marrais and Vedic Physics. Specifically, de Marrais discussed the concept of Lissajous Figures in relation to Sedenions and his 42 Assessors, in his first paper about Box Kites. Later, John Baez took up a related subject, the problem of epicycloids, apparently without having read the work of de Marrais. This paper examines this intersection between leading - edge mathematical physics and Vedic Physics in order to further illuminate the higher algebras - the Octonions, Sedenions and Trigintaduonions.

**Category:** Mathematical Physics

[197] **viXra:1309.0008 [pdf]**
*submitted on 2013-09-03 12:10:52*

**Authors:** Maknickas Algirdas Antano

**Comments:** 8 Pages.

It was proposed new gauge invariant Lagrangian, where the gauge field interact with the charged electromagnetic fields. Gauge invariance was archived by replacing of particle mass with new one invariant of the field $F_{\mu\nu}F^{\mu\nu}$ multiplied with calibration constant $\alpha_g$. It was shown that new proposed Lagrangian generates similar Dirac and electromagnetic field equations. Solution of Dirac equations for a free no massless particle answers to the 'question of the age' why free particle deal in experiments like a de Broil wave. Resulting wave functions of the new proposed Lagrangian will describe quantized list of bespinor particles of different masses. Finally, it was shown that renormalization of the new proposed Lagrangian is similar to QED in case similarity of new proposed Lagrangian to classic QED.

**Category:** Mathematical Physics

[196] **viXra:1309.0002 [pdf]**
*submitted on 2013-09-02 05:33:45*

**Authors:** José Francisco García Juliá

**Comments:** 1 Page.

The existence of the waves proves the existence of the special relativity.

**Category:** Mathematical Physics

[195] **viXra:1308.0140 [pdf]**
*submitted on 2013-08-27 09:54:56*

**Authors:** Malcolm Macleod

**Comments:** 3 Pages.

A set of formulas for gravity, atomic orbitals and the nucleus based on the Bohr model of the atom for n-orbitals are given. The formulas differ only in orbital velocity implying a common geometrical link. Analysis of the Rydberg formula suggests a mechanism whereby standing wave energy-wells form physical orbitals in the empty space between
particles. These orbitals are anti-photons; photons albeit of opposite phase. Via a simple
wave addition/subtraction, an incoming photon replaces the original orbital with the new orbital. The electron itself does not move. Gravitational waves become standing wave orbitals that are essentially extensions of atomic orbitals, they are both the orbital path and the orbital momentum. Potential and kinetic gravitational energies simply reflect the ratio of alignment of their motion vectors. Nucleus mass deficit and quantum entanglement may also be explained via this mechanism.

**Category:** Mathematical Physics

[194] **viXra:1308.0125 [pdf]**
*submitted on 2013-08-23 07:54:00*

**Authors:** Robert A. Herrmann

**Comments:** 31 Pages.

In this paper, a mathematical model for instruction-information, via instruction-sets, is presented and used as a fundamental aspect of the General Grand Unification Model (GGU-model), the only known mathematical cosmogony. A modern and differentiating nonstandard structure is employed to model this cosmogony, where a standardizing process produces a physical cosmology.

**Category:** Mathematical Physics

[193] **viXra:1308.0118 [pdf]**
*submitted on 2013-08-22 03:52:44*

**Authors:** Malcolm Macleod

**Comments:** 4 Pages.

A geometrical relationship between the charge constants, the fine structure constant alpha and the sqrt of Planck momentum is used to define G, h, e and electron mass me in terms of the 4 most accurate natural constants c, alpha, R and mu0 the vacuum permeability. As c and mu0 have exact values and the Rydberg constant R is precise to 12 digits, the accuracy of the calculated values for G, h, e and me is limited only by the precision of alpha. Results consistent with CODATA 2010 and suggest a digital Planck unit theory.

**Category:** Mathematical Physics

[192] **viXra:1308.0080 [pdf]**
*submitted on 2013-08-16 12:59:44*

**Authors:** Branko Zivlak

**Comments:** 5 Pages.

Abstract. Based on the methods, author used in previously published articles at viXra.org, Koide formula is corrected, to the results 2/3. The mass of tau lepton is also calculated.

**Category:** Mathematical Physics

[191] **viXra:1308.0069 [pdf]**
*submitted on 2013-08-13 09:56:13*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 10 Pages.

ABSTRACT: We Study the use of Abel summation applied to the evaluation of infinite series and infinite (divergent) integrals , we give several examples of how we can obtain a regularization for sums in the form and for divergent integrals in one and more variables

**Category:** Mathematical Physics

[190] **viXra:1308.0034 [pdf]**
*submitted on 2013-08-06 07:04:55*

**Authors:** Dan Visser

**Comments:** 20 Pages. A copy has been send to the Clay Mathematics Institute.

The Double Torus Hypothesis is a newly proposed cosmological model. It reaches further than quantum-dynamics. It are ‘sub-quantum dynamics’ in the Double Torus, which show how new insights lead to the solution of the Riemann hypothesis. The secret is the existence of the continuous recalculation by two additional time-clocks from below the Planck-scale. Several of my papers describe this additional time in a new dark energy-force formula. This formula shows that a quantum-Newton-force and a sub-quantum dark matter-space-force perform extreme small accelerations that function as the exponent of the number ‘e’, where it enables sub-quantum-vacuum to expand or contract. The clue to the solution of the Riemann hypothesis is, that these physics sub-quantum-accelerations connect with ’π’ for surfaces below the elementary quantum-surface. I show how the famous Euler-formula e^iπ +1=0 is related to that process and I also show this Euler-formula can be related to the Riemann hypothesis by expressing the prime-numbers in the inverse Riemann hypothesis. I relate that configuration to the divided structure of an elementary quantum-surface. This leads to a configuration that solves the Riemann hypothesis. So, now is the moment to announce how I did that. I realize this might be experienced as shocking, because I am an outsider: I’m an independent cosmologist. Hopefully my solution awards me with the 1 million USD-price by the Clay Mathematics Institute (this dated pdf-file has been send to the Clay Mathematics Institute).

**Category:** Mathematical Physics

[189] **viXra:1308.0018 [pdf]**
*submitted on 2013-08-04 10:05:46*

**Authors:** John Frederick Sweeney

**Comments:** 76 Pages.

The G2 Root system is the only root system in which the angle of pi / 6
appears between two roots. This is made necessary in nature by the
demand for circular objects which can be divided by six or twelve,
according to Vedic literature concerning the 28 Nakshastra or
astrological houses. In addition, G2 provides the key linkage between
the Sedenions, which curiously contain properties related to the
number 29 and the Octonions. G2 is key to the transformation from
Binary to Trinary,Fano Plane to Tetrahedron and the Sedenions, mixing
the 8 x 8 to 9 x 9 aspects of matter, or the Satwa and Raja aspects.
Finally, from the Sedenions this paper develops toward the Hopf
Fibration and the Boerdijk-Coxeter Helix, which is composed of
Sedenions in the form of tetrahedra. Along the way we travel all the
way back to the Osiris Temple of Abydos, Egypt, where G2 appears.

**Category:** Mathematical Physics

[188] **viXra:1307.0113 [pdf]**
*submitted on 2013-07-23 08:40:13*

**Authors:** Andrej Rehak

**Comments:** 9 Pages. The essay can be rated at FQXi's 2013 Essay Contest at http://fqxi.org/community/forum/topic/1876

If the result of the product of zero and infinity is not defined then the system located within dimensions of their ideas has no definition. On a scale between zero and infinity, we establish the system. Universally valid definition of its geometry of motion proves its validity. We prove that the system is. We establish a platform for its unification.

**Category:** Mathematical Physics

[187] **viXra:1307.0101 [pdf]**
*submitted on 2013-07-20 20:40:42*

**Authors:** John Frederick Sweeney

**Comments:** 16 Pages.

The concept of the Clifford Clock, which demonstrates the relationships between real, complex, quarternions and octonions, has become established in math physics. Less well-known are the spaces in which the algebras dwell. Space consists of an infinite number of tiny invisible cubes. Under the rubric of the Clifford Clock, these spaces take on significance, since the spaces themselves take on periodic aspects, and are directly related to Supersymmetry and the Super Brauer group of Lie Algebras. In addition, the Clifford Clock of Complex Spaces bears relevance to octagonal cuspid newforms, which are related to the Riemann Zeta Function.

**Category:** Mathematical Physics

[186] **viXra:1307.0100 [pdf]**
*submitted on 2013-07-20 14:31:05*

**Authors:** Andrew Nassif

**Comments:** 2 Pages.

Most people when thinking of the P vs. NP thinks of it as unsolved or unsolvable although it goes with a simple algorithmic proof in which I have written in my previous paper. Now as you may know, the P vs. NP can lead to some of the greatest breakthroughs in computer science, and mathematical physics. The question however asks you to use a method to figure out the complexity vs. non-complexity of a problem, which I have demonstrated in my last paper as the example of someone removing 100 possible students from a group of 400 and then coming up with the different combinations in which the 300 can’t be picked. This problem can be used in example with probability and solved through the complex equation where there is a solution for P equaling NP and you would then get ((400!)-(100!*3)). I gave this example using set theory and logic as well. This number would then be more than the number of atoms in the known planet in which we live on. However this is just one of the examples. My next example was an example of how some computers show through algorithms and polynomials that P does equal NP.

**Category:** Mathematical Physics

[185] **viXra:1307.0098 [pdf]**
*submitted on 2013-07-20 08:15:30*

**Authors:** M. H. Hassani

**Comments:** 10 Pages; 17 References. This work is accepted for publication in Galilean Electrodynamics Journal

Since OPERA is a very carefully designed experiment thus the sobering importance of its result, coupled with decades of some successful tests of special relativity theory (SRT) requires certain adjustment in our usual manner of thinking, and seriously prompts us to consider alternatives which should be consistent with both. To this end, we propose an alternative model as an explanation to the observed neutrino superluminality based on the universality of the well-known rest mass energy formula, and the idea that, at superluminal level, the velocity of a particle with real mass may be simultaneously dependent on its energy ratio and the kinematical attainability parameter. By raising this idea to the status of a hypothesis, we show that not only the OPERA result is very realistic but also is perfectly consistent with supernova SN1987a measurement. Consequently, SRT is not violated by the existence of superluminal particles since it is conceptually, physically and exclusively valid at subluminal level for relativistic velocities. As a direct consequence, the Minkowski space-time and Lorentz transformations are coherently extended to superluminal velocities.

**Category:** Mathematical Physics

[184] **viXra:1307.0045 [pdf]**
*submitted on 2013-07-08 12:34:00*

**Authors:** Maria de Guadalupe Caldera Cabral

**Comments:** 65 Pages. Thesis in Spanish

In this Thesis the formulae are presented for the relativistic products of
the matrices gamma_{\mu\nu} of Barut,Muzinich and Williams for the spin 1. They
are analogs of the Dirac matrices for the spin 1/2. They are found in the
2(2S+1) relativistic equations of Weinberg, Tucker and Hammer. Moreover, it was
proven that the mapping exists between the Proca vector-tensor formalism and
the 2(2S+1) formalism. The formulae of the relativistic products can be useful
in the calculations of the scattering amplitudes, cross-sections and the energy
spectra of the bound states for bosons.

**Category:** Mathematical Physics

[183] **viXra:1307.0030 [pdf]**
*submitted on 2013-07-06 05:17:19*

**Authors:** Klaus Lange

**Comments:** 10 Pages. 4 figures, written in german

Using the Heim-Droescher dimensions formular it will be shown that the number pair {p;n} = {57; 420} exist. With Heim QFT alone no meaning for this number pair is given. But with the delta-extended First-Word-Matrix it is shown that for all number pairs {1;2}, {2;2}, {4;6}, {6;12} and {57;420} topological classification numbers are given.

**Category:** Mathematical Physics

[182] **viXra:1307.0025 [pdf]**
*submitted on 2013-07-05 03:27:55*

**Authors:** Klaus Lange

**Comments:** 12 Pages. 2 figures, written in german

This paper shows that the prime number Apeiron according to Hedwig Cornad-Martius and Burkhard Heim is only a special case of parallel number sets. Based on the First-Word-Matrix from Michael König this leads to a structural supersymmetry and to other exotic particle properties. A calculation of the fine structure constant, the Weinberg angle and the mass of the stop-squark to 688+/-43 GeV/c^2 will be given.

**Category:** Mathematical Physics

[181] **viXra:1307.0024 [pdf]**
*submitted on 2013-07-04 20:19:45*

**Authors:** Jian-zhong Zhao

**Comments:** 4 Pages.

The Statement of Modified Saint-Venant’s Principle is suggested. The axisymmetrical deformation of the infinite circular cylinder loaded by an equilibrium system of forces on its near end is discussed and its formulation of Modified Saint-Venant’s Principle is established.
It is evident that finding solutions of boundary-value problems is a precise and pertinent approach to establish Saint-Venant type decay of elastic problems.

**Category:** Mathematical Physics

[180] **viXra:1307.0022 [pdf]**
*submitted on 2013-07-04 09:33:19*

**Authors:** Klaus Lange

**Comments:** 18 Pages. 2 figures, written in german

Based on the first-word-matrix, developed by Michael König, this paper shows how the entire 12 dimensional strucure according to Burkhard Heim theory is embedded into the G4 space matrix. The strucuture properties of complex relativity by Jean Emile Charon will be revealed using the Heim prime number space. A very good estimation of the fine structure constant will be made.

**Category:** Mathematical Physics

[179] **viXra:1306.0236 [pdf]**
*submitted on 2013-06-30 20:22:18*

**Authors:** Leonardo Pedro

**Comments:** 12 Pages. Draft version

The Majorana spinor is an element of a 4 dimensional real vector space. The Majorana
spinor representations of the Rotation and Lorentz groups are irreducible. The spinor
fields are space-time dependent spinors, solutions of the free Dirac equation.
We define the Majorana-Fourier transform and relate it to the linear momentum of a
spin one-half Poincare group representation. We show that the projective representation
of the Poincare group on the Majorana spinor field is orthogonal and irreducible. Using the Bargmann-Wigner equations, we study all orthogonal irreducible projective real
representations of the Poincare group, with finite or null mass and discrete spin.

**Category:** Mathematical Physics

[178] **viXra:1306.0231 [pdf]**
*submitted on 2013-06-28 19:36:33*

**Authors:** V. V.Dvoeglazov

**Comments:** 4 Pages. Presented in the DGFM-SMF School. December 2012. Puerto Vallarta, Mexico.

We construct self/anti-self charge conjugate (Majorana-like) states for the (1/2,0)+(0,1/2)$
representation of the Lorentz group, and their analogs for higher spins within the quantum field theory. The problem of the basis rotations and that of the selection of phases in the Dirac-like and Majorana-like field operators are considered. The discrete symmetries properties (P, C, T) are studied. Particular attention has been paid to the question of (anti)commutation of the Charge conjugation operator and the Parity in the helicity basis.
Dynamical equations have also been presented.
In the (1/2,0)+(0,1/2) representation
they obey the Dirac-like equation with eight components, which has been first introduced by Markov.
Thus, the Fock space for corresponding quantum fields is doubled (as shown by Ziino).
The chirality and the helicity
(two concepts which are frequently confused in the literature) for
Dirac and Majorana states have been discussed.

**Category:** Mathematical Physics

[177] **viXra:1306.0050 [pdf]**
*submitted on 2013-06-07 17:37:51*

**Authors:** Dan Visser

**Comments:** 4 Pages.

I found a ‘quadruple image’ of ‘Hot and Cold Spots’ in the CMB-image, published by the gathered data of the Planck-satellite in 2013, and analyzed by me in the context of the (new) Double Torus cosmology. The ‘quadruple image’ proves the Universe rotates!! The ‘quadruple image’ follows the logic of a ‘dark flow’ in the Double Torus. This ‘dark flow’ is expressed in my (new) dark energy force-formula and astronomically determined. Hence, the Double Torus (until now a hypothesis), is changing into “hitting the right spot”, or in other words: “starts being a real model” !! The new cosmology is extensively described in a series of papers of mine, hosted in the vixra-archive in the category Mathematical Physics.

**Category:** Mathematical Physics

[176] **viXra:1306.0026 [pdf]**
*submitted on 2013-06-06 05:33:35*

**Authors:** Sergey Kamenshchikov

**Comments:** 7 pages. Author is looking for postdoc position. kamphys@gmail.com

Evolution of arbitrary stochastic system was considered in frame of phase transition description. Concept of Reynolds parameter of hydrodynamic motion was extended to arbitrary complex system. Basic phase parameter was expressed through power of energy, injected into system and power of energy, dissipated through internal nonlinear mechanisms. It was found out that basic phase parameter as control parameter must be delimited for two types of system - accelerator and decelerator. It was suggested to select zero state entropy on through condition of zero value for entropy production. Zero state introduces universal principle of disorder characterization. On basis of self organization S – theorem we have derived relations for entropy production behavior in the vicinity stationary state of system. Advantage of these relations in comparison to classical Prigozhin theorem is versatility of their application to arbitrary nonlinear systems. It was found out that extended Prigozhin theorem introduces two relations for accelerator and decelerator correspondingly, which remarks their quantitative difference. At the same time classic Prigozhin theorem makes possible description of linear decelerator only. For unstable motion it corresponds to strange attractor.

**Category:** Mathematical Physics

[175] **viXra:1305.0202 [pdf]**
*submitted on 2013-05-31 12:24:22*

**Authors:** Nathan O. Schmidt

**Comments:** 22 pages; 6 figures; published in The Hadronic Journal, Volume 36, Number 1, February 2013

We propose a preliminary algorithm which is designed to reduce aspects of the n-body problem to a 2-body problem for holographic principle compliance. The objective is to share an alternative view-point on the n-body problem to try and generate a simple solution in the near future. The algorithm operates complex and triplex data structures to encode the chaotic dynamical system equipped with order parameter fields in both 3D and 4D versions of the Riemannian dual (fractional quantum Hall superfluidic) space-time topology. For the algorithm, we arbitrarily select one point-mass to be the origin and, from that reference frame, we subsequently engage a series of instructions to consolidate the residual (n-1)-bodies to a time-effective spherical surface. Through a step-by-step example, we demonstrate that the algorithm yields time-effective net-quantities that authorize us to define a time-effective potential, kinetic, and Lagrangian.

**Category:** Mathematical Physics

[174] **viXra:1305.0201 [pdf]**
*submitted on 2013-05-31 06:16:18*

**Authors:** Leonardo Pedro

**Comments:** 14 Pages.

The irreducibility of a representation of a real Lie algebra may
depend on whether the representation space is a real or complex
Hilbert space.
The unitary projective representations of the Poincare group on
complex Hilbert spaces were studied by Wigner and many
others. Although the Poincare group has a real Lie algebra, we do not
know of any study of the orthogonal projective representations of the
Poincare group on real Hilbert spaces.
The Majorana spinor field, a space-time dependent element of a 4
dimensional real vector space, is a solution of the free Dirac equation.
Our goal is to study the projective representation of the Poincare
group on the real Hilbert space of Majorana spinor fields.
The Majorana-Fourier and Majorana-Hankel orthogonal transforms of Majorana
spinor fields are defined and related to the linear and angular
momentums of a spin one-half projective representation of the Poincare
group.
Then we show that the projective representation of the Poincare group
on the Majorana spinor field, whether we include the parity and time
reversal or not, is orthogonal and irreducible.
This contrasts with the unitary projective representations of the
Poincare group on the Dirac and Weyl spinor fields, whose properties
change when including or excluding the parity and time reversal
transformations.

**Category:** Mathematical Physics

[173] **viXra:1305.0173 [pdf]**
*submitted on 2013-05-29 00:07:18*

**Authors:** John Frederick Sweeney

**Comments:** 5 Pages. Copyright John Frederick Sweeney 2013

Qi Men Dun Jia is an ancient form of divination from China which is still employed to make accurate predictions, and thus meets the definition of a scientific model based on scientific theory. This paper introduces a series of books which engages in "reverse engineering," using the concepts of contemporary mathematical physics to explain how this ancient model works. Specifically, we address Clifford Algebras, Bott Periodicity, Exceptional Lie Algebras, icosians, octonions and sedenions, as well as the Fano Plane and isometric relationships to Leptons and Baryons. The introduction concludes with reference to extremely ancient and superior science from 12,000 years ago, ancient Vedic culture and extremely ancient Egyptian culture.

**Category:** Mathematical Physics

[172] **viXra:1305.0171 [pdf]**
*submitted on 2013-05-29 04:29:28*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 15 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
•Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .

**Category:** Mathematical Physics

[171] **viXra:1305.0145 [pdf]**
*submitted on 2013-05-23 10:52:34*

**Authors:** Branko Zivlak

**Comments:** 5 Pages. 1 Table, 1 Appendix

This article is about relations between fundamental physical constants. The mass, radius and cycle of the universe are the basis for calculating Planck units.

**Category:** Mathematical Physics

[170] **viXra:1305.0137 [pdf]**
*submitted on 2013-05-22 22:25:06*

**Authors:** Jian-zhong Zhao

**Comments:** 14 Pages.

Zanaboni Theory is mathematically analyzed in this paper. The conclusion is that Zanaboni Theorem is invalid and not a proof of Saint-Venant's Principle; Discrete Zanaboni Theorem and Zanaboni's energy decay are inconsistent with Saint-Venant's decay; the inconsistency, discussed here, between Zanaboni Theory and Saint-Venant's Principle provides more proofs that Saint-Venant's Principle is not generally true.

**Category:** Mathematical Physics

[169] **viXra:1305.0136 [pdf]**
*submitted on 2013-05-22 22:34:09*

**Authors:** Jian-zhong Zhao

**Comments:** 8 Pages.

The problem of statement of Saint-Venant's Principle is concerned. Statement of Boussinesq or Love is ambiguous so that its interpretations are in contradiction with each other. Rationalized Statement of Saint-Venant’s Principle of elasticity is suggested to rule out the ambiguity of Statements of Boussinesq and Love. Rational Saint-Venant's Principle is suggested to fit and guide applications of the principle to fields of continuum physics and cover the analogical case as well as the non-analogical case discovered and discussed in this paper . `` Constraint-free " problems are suggested and `` Constraint-free " Rational Saint-Venant's Principle or Rational Saint-Venant's Principle with Relaxed Boundary Condition is developed to generalize the principle and promote its applications to fields of continuum physics . Applications of Analogical Rational Saint-Venant's Principle and `` Constraint-free " Rational Saint-Venant's Principle are exemplified, emphasizing `` properness " of the boundary-value problems. Three kinds of properly posed boundary-value problems, i.e., the boundary-value problem with the undetermined boundary function, the boundary-value problem with the implicit boundary condition and the boundary-value problem with the explicit boundary condition, are suggested for both `` constrained " and `` constraint-free " problems.

**Category:** Mathematical Physics

[168] **viXra:1305.0132 [pdf]**
*submitted on 2013-05-21 05:51:06*

**Authors:** Dan Visser

**Comments:** 6 Pages.

This article is about a new formula for dark energy force. This has already been published in a series of my articles in the archive vixra, but gets little attention. The new formula is part of a larger universe than the Big Bang, called the Double Torus hypothesis. The new dark energy force is different from dark energy in the Big Bang, because it uses the extension of time. This article emphases the extra time relating gravity and a new topology of quantum-spin of point particles, such as electrons. This article describes that cohesion by my dark energy force formula in a Double Torus Universe.

**Category:** Mathematical Physics

[167] **viXra:1305.0124 [pdf]**
*submitted on 2013-05-19 07:49:32*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages. 1st of six posters for the ICM 2 conference in Prague.

The following questions are raised in this document. First, can there be a stable (massive) graviton? If so, does this massive graviton, as modeled by KK DM, with a modification of slight 4 dimensional space mass, contribute to DE, at least in terms of re acceleration ? The answer, if one assumes that the square of a frequency for graviton mass is real valued and greater than zero appears to be affirmative. The author, when considering a joint DM – DE model finds evidence that re acceleration of the universe one billion years ago in a higher dimensional setting can be justified in terms of a slight modification of standard KK DM models, if one considers how an information exchange between present to prior universes occurs, which the author thinks mandates more than four dimensional space time geometry

**Category:** Mathematical Physics

[166] **viXra:1305.0123 [pdf]**
*submitted on 2013-05-19 07:52:54*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages. Poster or virtual paper for the ICM 2 conference

This paper uses the “Fjortoft theorem” for defining necessary conditions for instability. The point is that it does not apply in the vicinity of the big bang. We apply this theorem to what is called by T. Padmanabhan a thermodynamic potential which becomes would be unstable if conditions for the applications of “Fjortoft’s theorem” hold. In our case, there is no instability, so a different mechanism has to be appealed to. In the case of vacuum nucleation, we argue that conditions exist for the nucleation of particles as of the electroweak regime. Due to injecting material from a node point, in spacetime. This regime of early universe creation, coexits with the failure of applications of “Fjortoft” theorem in such a way as to give necessary and sufficient conditions for matter creation, in a way similar to the Higgs Boson

**Category:** Mathematical Physics

[165] **viXra:1305.0122 [pdf]**
*submitted on 2013-05-19 07:54:46*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

When initial radius R approaches zero if we use Stoica actually derived Einstein equations in a formalism which remove the big bang singularity pathology, then the reason for Planck length no longer holds. The implications of the initial radius approaching zero are the first part of this manuscript. Then the resolution is alluded to by work from Muller and Lousto, as to entanglement entropy implications of entanglement entropy. We present entanglement entropy in the early universe with a steadily shrinking scale factor, due to work from Muller and Lousto , and show that there are consequences due to initial entanged entropy for a time dependent horizon radius in cosmology, with for flat space conditions r(H)=conformal time. In the case of a curved, but not flat space version of entropy, we look at vacuum energy as proportional to the inverse of scale factor squared times the inverse of initial entropy, effectively when there is no initial time except with in line with the conformal time being almost zero. . The consequences for this initial entropy being entangled are elaborated in this manuscript. No matter how small the initial radial length gets, then for initial cosmological entropy if it is entanglement entropy, initial cosmological entropy will not go to zero.

**Category:** Mathematical Physics

[164] **viXra:1305.0121 [pdf]**
*submitted on 2013-05-19 07:56:51*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

First, we show through a numerical simulation that the massive Schwinger model used to formulate solutions to CDW transport is insufficient for transport of solitons (anti-solitons) through a pinning gap model of CDW transport. We show that a model Hamiltonian with Peierls condensation energy used to couple adjacent chains (or transverse wave vectors) permits formation of solitons (anti- solitons) which could be used to transport CDW through a potential barrier. We argue that there are analogies between this construction and the false vacuum hypothesis used for showing a necessary and sufficient condition for formation of CDW soliton – anti - soliton (S-S’) pairs in wave functionals presented in a prior publication

**Category:** Mathematical Physics

[163] **viXra:1305.0120 [pdf]**
*submitted on 2013-05-19 07:58:57*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

The author asks if octonion quantum gravity is relevant near the Planck scale. Furthermore, the question is raised if gravitational waves would be generated during the initial phase, , of the universe when an increase in degrees of freedom have in setting , so that the result can be observed by a gravitational detector.. The well appreciated .quantum gravity problem that the notion of a quantum state, representing the structure of spacetime at some instant, and the notion of the evolution of the state, does not get traction, since there are no real “instants”, is avoided by having the initial octonion geometry embedded in a larger, non linear “pilot model” (semi classical) embedding structure. The Penrose suggestion of re cycled space time avoiding a ‘big crunch’ is picked as the embedding structure, so as to avoid the ‘instants’ of time issue. In addition the favored idea is to avoid the well known string theory trap known as the dimensionality problem of an equation of motion (consistency condition) which is the reason why string theory dimensionality is either (10 or 26) depending upon if super symmetry is imposed. Getting octonion gravity as embedded in a larger, Pilot theory embedding structure may restore Quantum Gravity to its rightful place in early cosmology without the lunacy of then afterwards ‘Schrodinger equation ‘ states of the universe, forevermore afterwards. Setting , in a GW detector due to appropriate measurement procedures may allow the opportunity to find experimental clues as to this embedding structure in which octonion gravity may emerge in the Planckian regime.of evolutionary cosmology

**Category:** Mathematical Physics

[162] **viXra:1305.0118 [pdf]**
*submitted on 2013-05-19 08:00:58*

**Authors:** Andrew Beckwith

**Comments:** 4 Pages.

The following questions is asked, If one takes the covariant derivative of a Stress-energy representation of early universe massive gravitons, is the derivative of the Graviton stress tensor equal to zero ? If so, then in what range of astrophysics does this occur, and when does this formalism break down? Lavenda and Davies argued that the derivative of a generalized GR stress energy tensor being zero in itself is insufficient to show that the 1st law of thermodynamics alone holds. If the full Stress-Energy tensor expression for GR is written out, there is a stress energy tensor component involving GW alone which we highlight. The problem as to this test is if the derivative of the Stress energy tensor, for gravitons as written by Visser is brought up. This Visser stress energy tensor for massive gravitons will not even satisfy the 1st thermodynamic law. We bring this up as a counter point to an article written by Lavenda and Davies purporting to claim that the Tolman test for a first law of thermodynamics which they generalize to first and second law of thermodynamics for inflationary cosmology. We show a breakdown of a zero value for the derivative of the Stress energy tensor for early universe massive gravitons and this derivative of the massive Graviton Stress energy tensor (Visser) will not even satisfy the first law of thermodynamics according to the Tolman criteria. Note that if the Visser Massive Graviton Stress energy tensor scenario does not hold then the Lavenda and Davies objection to inflation is upheld.

**Category:** Mathematical Physics

[161] **viXra:1305.0100 [pdf]**
*submitted on 2013-05-17 03:47:11*

**Authors:** Maurizio M. D'Eliseo

**Comments:** 13 Pages.

Orbital averages are employed to compute the secular variation of the elliptical planetary elements
in the orbital plane in presence of perturbing forces of various kinds. They are also useful as an
aid in the computation of certain complex integrals. An extensive list of computed integrals is given.

**Category:** Mathematical Physics

[160] **viXra:1305.0099 [pdf]**
*submitted on 2013-05-16 08:37:03*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 6 Pages.

We have analyzed, calculated and extended the modification of Maxwell’s equations in a complex Minkowski metric, M4 in a C2 space using the SU2 gauge, SL(2,c) and other gauge groups, such as SUn for n >2 expanding the U1 gauge theories of Weyl. This work yields additional predictions beyond the electroweak unification scheme. Some of these are: 1) modified gauge invariant conditions, 2) short range non-Abelian force terms and Abelian long range force terms in Maxwell’s equations, 3) finite but small rest of the photon, and 4) a magnetic monopole like term and 5) longitudinal as well as transverse magnetic and electromagnetic field components in a complex Minkowski metric M4 in a C4 space.

**Category:** Mathematical Physics

[159] **viXra:1305.0085 [pdf]**
*submitted on 2013-05-14 14:42:59*

**Authors:** Nathan O. Schmidt

**Comments:** 16 pages, 2 figures, published in the Hadronic Journal

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.

**Category:** Mathematical Physics

[158] **viXra:1305.0071 [pdf]**
*submitted on 2013-05-12 06:33:07*

**Authors:** Dan Visser

**Comments:** 2 Pages.

The Higgs-particle could be a dark matter particle! It is not enough to confirm spin 0 and + parity for the Higgs-like particle to let it be the Higgs-particle. The Double Torus hypothesis should be involved. A dark matter particle in this new framework could also have spin 0 and + parity under condition it contributes to gravity, but its properties can also contribute as negative mass to anti-gravity.

**Category:** Mathematical Physics

[157] **viXra:1305.0056 [pdf]**
*submitted on 2013-05-08 15:06:47*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 19 Pages.

We develop a formalism for the Schrödinger equation in an eight
dimensional complex Minkowski space and discuss its relation to the Dirac equation,
properties of nonlocality, remote connectedness, Young’s double slit experiment, Bell’s
Theorem, the EPR paradox and anticipatory parameters of spacetime; and also identify
an imaginary temporal component as a small nonlinear term and find soliton or solitary
wave solutions. These coherent solutions can carry information over long distances, are
consistent with Lorentz invariance and appear to provide a fundamental methodology
for describing the issue of quantum measurement and a new context for the basis of
quantum theory. In the Copenhagen view models of reality are not desirable. However
our new approach may enable the redefinition of concepts of reality from a new
nonlocal anticipatory quantum theory. Certainly the most desirable consequence of
scientific discovery is the ability to redefine our concepts of reality.

**Category:** Mathematical Physics

[156] **viXra:1305.0055 [pdf]**
*submitted on 2013-05-08 15:09:12*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 25 Pages.

Many naturally occurring phenomena require theoretical treatment
utilizing complex analysis by methods such as the Cauchy-Riemann relations using
hyper-geometrical spaces which treat inherently nonlinear, non-dispersive,
collective nonlocal resonant states of a quantum system, so as to be consistent with
the nonlinearity inherent in General Relativity. Typical quantum approaches form
linear approximations limiting the ability to formulate a quantum consistent
Relativity Theory.

**Category:** Mathematical Physics

[155] **viXra:1305.0049 [pdf]**
*submitted on 2013-05-08 06:04:29*

**Authors:** Andrej Rehak

**Comments:** 4 Pages.

Geometric demonstration of free fall and rotation reveals space-time nature of the genesis of circle. We show that the operations with radius are equivalent to operations with velocity. Consequently, conventional spatial unit for radius (m), becomes equivalent to dynamic space-time unit for speed (m/s). We prove that the velocity is a physical equivalence of geometric idea of radius.

**Category:** Mathematical Physics

[154] **viXra:1305.0048 [pdf]**
*submitted on 2013-05-08 06:10:03*

**Authors:** Andrej Rehak

**Comments:** 8 Pages.

Geometric demonstration located in v, t diagram explains the nature of the period of a pendulum, i.e. the universal connection of time with velocity (radius) and acceleration. Conceptual nature of the principles proof points to its universal validity. In other words, if it is valid for a circle, it is valid. Through the geometry of free fall we describe physical nature of irrational numbers π and √2. We demonstrate physical matrix of scale √2nπ. Through the relationship between the variables of space, time and velocity, using the principle of the pendulum, we illustrate the foundation of the law of conservation of energy. Analyzing its motion we point to nature of distortion of Euclidean geometry.

**Category:** Mathematical Physics

[153] **viXra:1305.0033 [pdf]**
*submitted on 2013-05-05 00:05:04*

**Authors:** Temur Z. Kalanov

**Comments:** 8 Pages.

Critical analysis of the generally accepted (standard) foundations of differential and integral calculus is proposed. Methodological basis of the analysis is the unity of formal logic and of rational dialectics. It is shown that the generally accepted foundations are based on the logically and practically erroneous concepts “infinitesimal quantity (uninterruptedly diminishing quantity)”, “derivative”, “derivative as function of variable quantity” and, consequently, represent incorrect basis of mathematics and of theoretical physics.

**Category:** Mathematical Physics

[152] **viXra:1305.0032 [pdf]**
*submitted on 2013-05-05 00:09:30*

**Authors:** Temur Z. Kalanov

**Comments:** 10 Pages.

The critical analysis of the Pythagorean theorem and of the problem of irrational numbers is proposed. Methodological basis for the analysis is the unity of formal logic and of rational dialectics. It is shown that: 1) the Pythagorean theorem represents a conventional (conditional) theoretical proposition because, in some cases, the theorem contradicts the formal-logical laws and leads to the appearance of irrational numbers; 2) the standard theoretical proposition on the existence of incommensurable segments is a mathematical fiction, a consequence of violation of the two formal-logical laws: the law of identity of geometrical forms and the law of lack of contradiction of geometrical forms; 3) the concept of irrational numbers is the result of violation of the dialectical unity of the qualitative aspect (i.e. form) and quantitative aspect (i.e. content: length, area) of geometric objects. Irrational numbers represent a calculation process and, therefore, do not exist on the number scale. There are only rational numbers.

**Category:** Mathematical Physics

[151] **viXra:1305.0031 [pdf]**
*submitted on 2013-05-05 00:13:38*

**Authors:** Temur Z. Kalanov

**Comments:** 11 Pages.

The work is devoted to solution of an actual problem – the problem of relation between geometry and natural sciences. Methodological basis of the method of attack is the unity of formal logic and of rational dialectics. It is shown within the framework of this basis that geometry represents field of natural sciences. Definitions of the basic concepts "point", "line", "straight line", "surface", "plane surface", and “triangle” of the elementary (Euclidean) geometry are formulated. The natural-scientific proof of the parallel axiom (Euclid’s fifth postulate), classification of triangles on the basis of a qualitative (essential) sign, and also material interpretation of Euclid’s, Lobachevski’s, and Riemann’s geometries are proposed.

**Category:** Mathematical Physics

[150] **viXra:1305.0010 [pdf]**
*submitted on 2013-05-01 19:19:35*

**Authors:** R.L. Amoroso, L.H. Kauffman, E.A. Rauscher, P. Rowlands J-P Vigier

**Comments:** 27 Pages.

Recent attempts to consider isolated particles and real constitutive wave elements as localized,
extended spacetime structures (i.e., moving within time-like hypertubes or branes are developed within a causal
extension of the Feynman-Gell-Mann electron model. These extended structures contain real internal motions,
(i.e., internal hidden parameters) locally correlated with the "hidden parameters" describing the local collective
motions of the corresponding pilot-waves. Recent experimental evidence is briefly discussed.

**Category:** Mathematical Physics

[149] **viXra:1305.0009 [pdf]**
*submitted on 2013-05-01 19:35:02*

**Authors:** Richard L. Amoroso, Elizabeth A. Rauscher

**Comments:** 18 Pages.

Here we present discussion for the utility of resonant interference in Calabi-Yau mirror symmetry as a
putative empirical test of the existence of virtual tachyon / tardon interactions in a covariant Dirac polarized vacuum

**Category:** Mathematical Physics

[148] **viXra:1304.0163 [pdf]**
*submitted on 2013-04-29 14:51:49*

**Authors:** Andrew Nassif

**Comments:** 2 Pages.

This problem has been solved by me over a year ago, and published. Today I am posting a more complex and complicated version, yet put in Layman terms. I hope by doing this it will garner the attention of Clay Mathematics as well as show logical input on its mathematical endeavors.

**Category:** Mathematical Physics

[147] **viXra:1304.0152 [pdf]**
*submitted on 2013-04-26 14:13:20*

**Authors:** Jeremy Dunning-Davies.

**Comments:** 6 Pages.

Here an introduction to Wesley’s neomechanics is presented. It is shown to produce some of the same results as Special Relativity but without both the mathematical and philosophical basis of that subject. As with other work in which results associated with General Relativity are obtained without recourse to the fundamental bases of that subject, so here too the pre-eminent place afforded Special Relativity in modern science is called into question. The opportunity is taken to extend Wesley’s ideas to the case where the mass of the body when at rest is not constant.

**Category:** Mathematical Physics

[146] **viXra:1304.0106 [pdf]**
*submitted on 2013-04-21 22:33:04*

**Authors:** Vyacheslav Telnin

**Comments:** 6 Pages.

This paper deals with the generalizations of the First Noether theorem. It takes into
account not only the first derivatives of the fields by the coordinates in Lagrangian, but
also the second. And this theorem is generalized on the curved spaces. And also it's
generalized on asymmetric metric tensors.

**Category:** Mathematical Physics

[145] **viXra:1304.0051 [pdf]**
*submitted on 2013-04-10 15:49:46*

**Authors:** Branko Zivlak

**Comments:** 4 Pages. 1 Table

This article is about relations between fundamental physical constants.

**Category:** Mathematical Physics

[144] **viXra:1304.0010 [pdf]**
*submitted on 2013-04-03 02:57:32*

**Authors:** Dan Visser

**Comments:** 13 Pages.

The Double Torus hypothesis stands for a new architecture for the Universe, which means another dark energy as dynamics and no Big Bang. New dark energy-time is applied to dark matter. It is ‘extra time’ originated from a time-scale smaller than the Planck-time. The implication is a Double Torus of the dark energy-time enclosing and intertwining an inner dark matter torus. It might sound controversial, but a new ‘dark energy-force formula’ in the hypothesis enables to make calculations, which match the observed dark matter-accelerations in galaxies and the Pioneer satellites 1 and 2. This new formula relates to Newton quantum-gravity force and dark matter-force both implemented in one product. The dark matter force could be gravitational (+) and anti-gravitational (-). The formula also sets the laboratory acceleration-limit for Newton-gravity, 5 x 10^-14 m/s^2, to a theoretically lower value of 2.8659 x10^-14 m/s^2. There is no other formula, or theory, to do that. The hypothesis-dynamic is developed by DAN Visser, Almere, the Netherlands, an independent cosmologist. Additional evidence comes from astronomical observations: Such as the asymmetry in the Cosmic Microwave Background (CMB) and a ‘Dark Flow’, which pleads for a cyclic-curved torus-shape of the universe. This also could explain the observed ‘cold spot’ in the CMB by to imagine dark matter is disappearing in the far end of the curved torus-shape. Hence, also a ‘hot spot’ in the CMB should exist. This should correspond to the approaching dark flow coming from the other curved torus far-end.

**Category:** Mathematical Physics

[143] **viXra:1303.0209 [pdf]**
*submitted on 2013-03-28 04:10:29*

**Authors:** Branko Zivlak

**Comments:** 8 Pages. 11 relations, 1 figure

This paper is about relations between the mass of universe and mass of some elementary particles. Important is only the diagram in Figure 1, which you can understand in any language if you know the language of mathematics and physics.

**Category:** Mathematical Physics

[142] **viXra:1303.0167 [pdf]**
*submitted on 2013-03-22 15:28:17*

**Authors:** Yingqiong Gu

**Comments:** 3 Pages.

It is a hot topic about how to trade a stock/group of stocks in a non-news day. Author tries to design safe, profitable automated stock trading agents using evolutionary algorithms[2].
In quantum mechanics, perturbation theory[4] is a set of approximation schemes directly related to mathematical perturbation for describing a complicated quantum system in terms of a simpler one. The idea is to start with a simple system for which a mathematical solution is known, and add an additional "perturbing" Hamiltonian representing a weak disturbance to the system. If the disturbance is not too large, the various physical quantities associated with the perturbed system (e.g. its energy levels and Eigen states) can, from considerations of continuity, be expressed as 'corrections' to those of the simple system. These corrections, being 'small' compared to the size of the quantities themselves, can be calculated using approximate methods such as asymptotic series. The complicated system can therefore be studied based on knowledge of the simpler one.
In Stock Market, for a non-news trading day, stock prices will mostly depend on the initial price at given time, and bid-ask spread.

**Category:** Mathematical Physics

[141] **viXra:1303.0152 [pdf]**
*submitted on 2013-03-21 04:22:55*

**Authors:** Markos Georgallides

**Comments:** 22 Pages.

Point , which is nothing and has not any Position , may be anywhere in Space , therefore the Primary point A , being nothing also in no Space , is the only Point and nowhere i.e. Primary Point is the only Space and from this all the others , so then this primary point A to exist at a second point B somewhere else , point A must move at point B , where then A ≡ B . Presupposition for Unit AB = ds means an Impulse P removes point A to B and since in each Restrained System (S) the Work done ( W ) by Impulse P on a Virtual displacement ( ds > 0) is zero , and then W = ∫ A-B [ P.ds ] = 0 → [ ds .( PA+P B ) = 0 ] and Point A is in Space [S] and point B is in Anti-Space [aS] which are self created and are Property and Essence from the same Unit AB, therefore these are also a Restrained System(S). Since the only two Elements of Universe are ds and P and are connected by Virtual Work Principle and since Unit AB = ds is a quantized dimension,so Impulse is also quantized.Quantization of Points becomes through Vector Unit dš = ÃB which is the first dimensional Unit [ Zenon Paradox 13]and this because Vector has Position and Direction .Quantization of Energy is done in bound States ( loops ) because bound states [11-16] withhold diffusion ( flow ) .The two fundamental dimensions
( quanta of Points (ds) and quanta of Energy (dP) , are connected on Primary dipole and on any dipole AiBi . [PNS] is self created and consists a space (x,y,z) Scalar field Sp which constructs a vector field Sa = Ñ.Sp . The position of dipole in the equilibrium Space Anti-Space keeps charge = momentum ( Energy→ the difference of primary Work which is bounded on edge points ) and Angular momentum ( Spin → angular momentum is the intrinsic twist of Space , Anti-Space ) which inextricably unify geometry of Space and motion . On any Dipole AB of [PNS] with dš = ( [J,E,B] and content © ) ,where motion occurs only as (+) → (-) Source (+) → Drain (-) ,Conservation State of Work exists on magnitude |dš| = √ J² + E² + B² of vector ř ( J,E, B ) ( which is the Sub-Space of AB ) and on the two perpendicular Fields Ê = Ñx J , B = Ñx Ê ( which are the two diffused equilibrium Spaces and Anti -Spaces of AB , Ñx Ê = 0 , Ñ x B = 0 ) . Since,Source (+) →Drain (-) , in [PNS] is the equilibrium of Space [S] and Anti-Space [aS] , therefore the only magnitude for motion is J , while E and B are produced , as this happens in the Magnetic fields where lines ( loops ) close in themselves and this because no sources exist ↑→ ® for magnetic fields B and so the two models [ the B-field Pole and Amperian loop ] are explained. Solving equation ds.( PA+ PB ) = 0 then ds.PA = - ds.PB and since , dš , is constant for Primary dipole , so the Work conserved on every point in Spaces is constant and equal to [ dš .Impulse P = constant ] . i.e. The applied Work [ Wi → 1 → ∞ ] = ( charge ± P ) on every point of the three , Spaces , Anti–Spaces and Sub–Spaces , which coexist in [PNS] is conserved on Points , meaning that every point of [PNS] consist the fundamental ± Scalar Field with variables the Constraint Forces and Angular momentum [ Spin = Wij →1→ ∞] , and is conserved always in [PS] , [ PaS] or, The two elements [Vector dš = AB (matter) , ± dP ,Work p , Spin = momentum ] of the Infinite Dipole Vectors [AB] = [ ĀB – PA , PB ] build Particles with Identity Card , the Constant Product → dš . p = constant …(k) ← so , the Possible Energy Range (m) Scales , of the two fundamental and quantized dimensions [ ds , - P , + P ] are the three Layers ,
(- i ) ↔ (0 ) = - P → [ ds , - P , ] → Black Holes Scale = k 1 → ds 1. dP 1 = k 1
(-i ) ↔ (+i) = 7 P → [ ds , - P , + P ] → Planck Scale Matter = k 2 → ds 2. dP 2 = k 2
(+i ) ↔ (0 ) = + P → [ ds , + P , ] → Dark Matter Scale = k 3 → ds 3. dP 3 = k 3
For any single particle of wavelength λ = ds and dP = Charge → momentum ( p ) exists :
dš.dP = λ . p = constant = h → is the reduced Planck constant in Planck Scale Matter . For ds near zero and P = ∞ , is needed a new Type of Light to see what is happening below Planck length Level , Layer 10¯35 m .Primary Vector monad and Vector monads are , either Static ( equilibrium ) or Dynamic ( are moving ) , and keep their Conservation of State ( The Total work is equal to zero ) in the three equilibrium and perpendicular monads [ J , E , B ] which are in Subspaces , Spaces , Anti-Spaces ( and thus , not turn
to non-existence ) and are interchanged by Pythagoras conservation law of Volume.
The geometric concepts of [PNS] as two dimensional field is that , the third dimension represents the amplitude of the potential S . Considering x-y Plane as the base and the vertical (z) is the potential S , then contours of constant potential altitudes of [PNS] are Cylindrical or Solenoidal and for Position 0 ( which is the equilibrium Horizon of Space and anti-Space) is Sphere , therefore [PNS] with the included Space [S] and Anti-Space [aS] may be Sphere and Solenoidal simultaneously.

**Category:** Mathematical Physics

[140] **viXra:1303.0134 [pdf]**
*submitted on 2013-03-18 12:13:37*

**Authors:** Dan Visser

**Comments:** 8 Pages.

New gravity-physics and -mathematics produce calculations of dark matter-accelerations and prove we live in a Double Torus Universe, which recalculates Quantum Gravity in vacuum. The set of equations to do that, prove the (new) dark energy force formula in the Double Torus Hypothesis is correct. The formula has been developed step by step and described in my Vixra-papers. It is an alternative for still unknown dark energy used in Big Bang cosmology. It is a tool for the awareness that the universe is not a universe that started with a Big Bang. The universe is a Double Torus, which uses + and - dark matter force to change quantum-gravity. The formula shows clearly a new view on the universe to be necessary. This paper shows theoretical predictions through calculations that match the experimental values of dark matter-accelerations in galaxies, the Pioneer-satellites (1 and 2) and produces the lowest limit for Newton-gravitational force. This Newton limit-acceleration matches the laboratory-experiments and moreover sets the limit to a slightly theoretical lower limit-acceleration of 2.8659 x 10^-14 [m/s2]. There is no other theory that predicts this limit. The conditions of the formula show, that quantum-gravity is related to a dark matter force. Dark energy-time from below the Planck-time is applied to the dark matter.

**Category:** Mathematical Physics

[139] **viXra:1303.0090 [pdf]**
*submitted on 2013-03-12 08:23:19*

**Authors:** Florentino Muñiz Ania

**Comments:** 2 Pages. Spanish.

This article shows how the gravitational force is conservative only in ideal models of small
size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems.
Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general, no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos.

**Category:** Mathematical Physics

[138] **viXra:1303.0008 [pdf]**
*submitted on 2013-03-02 12:49:28*

**Authors:** Branko Zivlak

**Comments:** 7 Pages. 15 relations, 1 table, 1 figure

Abstract. In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsacker's (1912-2007) relationships between the fundamental physical constants. The first section examines Sollinger's the relationship between the masses of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory.

**Category:** Mathematical Physics

[137] **viXra:1303.0003 [pdf]**
*submitted on 2013-03-01 15:56:25*

**Authors:** Sergey V. Ershkov

**Comments:** 5 Pages. Keywords: Helmholtz equation, PWE, paraxial approximation, bipolar coordinates

A new type of exact solution of the reduced 3 dimensional spatial PWE (paraxial wave equation) for the case of bipolar coordinates is presented here.
First, we consider a self-similar representation of the solution in a bipolar coordinate system, the second we additionally reduce PWE under a proper paraxial assumption.
Analyzing the structure of the final equation, we obtain the simple exact solution which is proved to satisfy to such an equation in bipolar coordinates.
Besides, there is a limitation of the components of self-similar solution of a new type.

**Category:** Mathematical Physics

[136] **viXra:1302.0154 [pdf]**
*submitted on 2013-02-24 10:16:15*

**Authors:** Branko Zivlak

**Comments:** pages 7+7, language Serbian+Italian, 15 formulas, 1Table, 1 picture

Abstract. In "The Code of Nature" [1] Helmut Söllinger gives his and Carl Friedrich von Weizsäcker's (1912-2007) the relationship between the fundamental physical constants. The first section examines the relationship between the mass of protons and electrons, and the fundamental physical constants. The second is about the Weizsacker's assumption of proportionality between the Planck length, Compton wavelength and radius of the Universe. In the third section, I try to explain, the previous relationships, in light of the attractive-repulsive forces of the Ruđer Bošković (1711-1787), the earliest founder of quantum theory. This version is written, in the lenguages, Bošković’s father and mother.

**Category:** Mathematical Physics

[135] **viXra:1302.0132 [pdf]**
*submitted on 2013-02-19 21:26:30*

**Authors:** Zhanqiang Bai, Guowu Meng, Erxiao Wang

**Comments:** 13 Pages.

It is demonstrated that, for the recently introduced classical magnetized Kepler problems in dimension $2k+1$, the non-colliding orbits in the ``external configuration space" $\mathbb R^{2k+1}\setminus\{\mathbf 0\}$ are all conics, moreover, a conic orbit is an ellipse, a parabola, and a branch of a hyperbola according as the total energy is negative, zero, and positive. It is also demonstrated that the Lie group ${\mr {SO}}^+(1,2k+1)\times {\bb R}_+$ acts transitively on both the set of oriented elliptic orbits and the set of oriented parabolic orbits.

**Category:** Mathematical Physics

[134] **viXra:1302.0112 [pdf]**
*submitted on 2013-02-17 02:09:57*

**Authors:** M. Pitkanen

**Comments:** 7 Pages.

I have been reading two highly interesting articles by Robert Kiehn. There are very many contacts on TGD inspired vision and its open interpretational problems.
The notion of Falaco soliton has surprisingly close resemblance with K\"ahler magnetic flux tubes defining fundamental structures in TGD Universe. Fermionic strings are also fundamental structures of TGD accompanying magnetic flux tubes and this supports the vision that these string like objects could allow reduction of various condensed matter phenomena such as sound waves -usually regarded as emergent phenomena allowing only highly phenomenological description - to the fundamental microscopic level in TGD framework. This can be seen as the basic outcome of this article.
Kiehn proposed a new description for the generation of various instability patterns of hydrodynamics flows (Kelvin-Helmholtz and Rayleigh-Taylor instabilities) in terms of hyperbolic dynamics so that a connection with wave phenomena like interference and diffraction would emerge. The role of characteristic surfaces as surfaces of tangential and also normal discontinuities is central for the approach. In TGD framework the characteristic surfaces have as analogs light-like wormhole throats at which the signature of the induced 4-metric changes and these surfaces indeed define boundaries of two phases and of material objects in general. This inspires a more detailed comparison of Kiehn's approach with TGD.

**Category:** Mathematical Physics

[133] **viXra:1302.0110 [pdf]**
*submitted on 2013-02-17 02:17:26*

**Authors:** M. Pitkanen

**Comments:** 40 Pages.

The original focus of this article was p-adic icosahedron. The discussion of attempt to define this notion however leads to the challenge of defining the concept of p-adic sphere, and more generally, that of p-adic manifold, and this problem soon became the main target of attention since it is one of the key challenges of also TGD.
There exists two basic philosophies concerning the construction of both real and p-adic manifolds: algebraic and topological approach. Also in TGD these approaches have been competing: algebraic approach relates real and p-adic space-time points by identifying the common rationals. Finite pinary cutoff is however required to achieve continuity and has interpretation in terms of finite measurement resolution. Canonical identification maps p-adics to reals and vice versa in a continuous manner but is not consistent with p-adic analyticity nor field equations unless one poses a pinary cutoff. It seems that pinary cutoff reflecting the notion of finite measurement resolution is necessary in both approaches. This represents a new notion from the point of view of mathematics.
a) One can try to generalize the theory of real manifolds to p-adic context. The basic problem is that p-adic balls are either disjoint or nested so that the usual construction by gluing partially overlapping spheres fails. This leads to the notion of Berkovich disk obtained as a completion of p-adic disk having path connected topology (non-ultrametric) and containing p-adic disk as a dense subset. This plus the complexity of the construction is heavy price to be paid for path-connectedness. A related notion is Bruhat-Tits tree defining kind of skeleton making p-adic manifold path connected. The notion makes sense for the p-adic counterparts of projective spaces, which suggests that p-adic projective spaces (S^{2} and CP_{2} in TGD framework) are physically very special.
b) Second approach is algebraic and restricts the consideration to algebraic varieties for which also topological invariants have algebraic counterparts. This approach looks very natural in TGD framework - at least for imbedding space. Preferred extremals of Kähler action can be characterized purely algebraically - even in a manner independent of the action principle - so that they might make sense also p-adically.
Number theoretical universality is central element of TGD. Physical considerations force to generalize the number concept by gluing reals and various p-adic number fields along rationals and possible common algebraic numbers. This idea makes sense also at the level of space-time and of "world of classical worlds" (WCW).
Algebraic continuation between different number fields is the key notion. Algebraic continuation between real and p-adic sectors takes place along their intersection which at the level of WCW correspond to surfaces allowing interpretation both as real and p-adic surfaces for some value(s) of prime p. The algebraic continuation from the intersection of real and p-adic WCWs is not possible for all p-adic number fields. For instance, real integrals as functions of parameters need not make sense for all p-adic number fields. This apparent mathematical weakness can be however turned to physical strength: real space-time surfaces assignable to elementary particles can correspond only some particular p-adic primes. This would explain why elementary particles are characterized by preferred p-adic primes. The p-adic prime determining the mass scale of the elementary particle could be fixed number theoretically rather than by some dynamical principle formulated in real context (number theoretic anatomy of rational number does not depend smoothly on its real magnitude!).
Although Berkovich construction of p-adic disk does not look promising in TGD framework, it suggests that the difficulty posed by the total disconnectedness of p-adic topology is real. TGD in turn suggests that the difficulty could be overcome without the completion to a non-ultrametric topology. Two approaches emerge, which ought to be equivalent.
a) The TGD inspired solution to the construction of path connected effective p-adic topology is based on the notion of canonical identification mapping reals to p-adics and vice versa in a continuous manner. The trivial but striking observation was that canonical identification satisfies triangle inequality and thus defines an Archimedean norm allowing to induce real topology to p-adic context. Canonical identification with finite measurement resolution defines chart maps from p-adics to reals and vice versa and preferred extremal property allows to complete the discrete image to hopefully space-time surface unique within finite measurement resolution so that topological and algebraic approach are combined. Finite resolution would become part of the manifold theory. p-Adic manifold theory would also have interpretation in terms of cognitive representations as maps between realities and p-adicities.
b) One can ask whether the physical content of path connectedness could be also formulated as a quantum physical rather than primarily topological notion, and could boil down to the non-triviality of correlation functions for second quantized induced spinor fields essential for the formulation of WCW spinor structure. Fermion fields and their n-point functions could become part of a number theoretically universal definition of manifold in accordance with the TGD inspired vision that WCW geometry - and perhaps even space-time geometry - allow a formulation in terms of fermions. This option is a mere conjecture whereas the first one is on rigorous basis.

**Category:** Mathematical Physics

[132] **viXra:1302.0059 [pdf]**
*submitted on 2013-02-09 17:05:12*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Helmholtz equation, paraxial approximation, Gaussian beam

A new type of exact solution of the full 3 dimensional spatial Helmholtz equation for the case of non-paraxial Gaussian beams is presented here.
We consider appropriate representation of the solution for Gaussian beams in a spherical coordinate system, then implement it in the full 3 dimensional Helmholtz Eq.
Analyzing the structure of the final equation, we obtain one of the simple exact solutions which is proved to satisfy to such an equation for Gaussian beams.
Also the proper examples of implementing of the paraxial approximation for Gaussian beam could easily be obtained for a new type of exact solution of Helmholtz equation.

**Category:** Mathematical Physics

[131] **viXra:1302.0020 [pdf]**
*submitted on 2013-02-04 05:20:58*

**Authors:** Chun-Xuan Jiang

**Comments:** 13 Pages.

We make the new periodic table of elements 1-92

**Category:** Mathematical Physics

[130] **viXra:1301.0158 [pdf]**
*submitted on 2013-01-26 07:14:47*

**Authors:** Dan Visser

**Comments:** 6 Pages.

The Double Torus, a new hypothesis for the universe, has been put in perspective and related to other theories and hypotheses. This ‘paper’ could be used by the press. The Double Torus hypothesis is theoretically and mathematically-physics-based. Examples of evidence might be available already.

**Category:** Mathematical Physics

[129] **viXra:1301.0139 [pdf]**
*submitted on 2013-01-22 05:11:06*

**Authors:** Branko Zivlak

**Comments:** 9 Pages. 25 relations

Abstract. The aim of this article is to determine dimensionless physical constants through mathematical constants and other dimensionless physical constants.

**Category:** Mathematical Physics

[128] **viXra:1301.0110 [pdf]**
*submitted on 2013-01-18 10:51:52*

**Authors:** Helmut Söllinger

**Comments:** Pages. e-mail adress of the author: 64.soellinger@aon.at

The scope of the work described in this paper is a systematic investigation as to whether or not the mass of the proton and the electron can be represented by other fundamental constants. The author arrives at the conclusion that the mass of the proton and the electron can be expressed by a combination of five constants that occur in nature; namely, e, εo, h, c, G, plus a time-variable parameter. In this context, the author has studied more than 37,000 options using electronic support and powering the fundamental constants with natural numbers only.
The simplest and most convincing formula the author has found is:
me3 x mp3 = (e2 h/4p εo c G R)2
This equation results in the exact value of the mass of the proton and the electron. The beauty and simplicity of this equation give rise to the following question: What, if not this formula, is able to represent the mass of the two most important particles?
The author’s conclusion is that either the electron and proton masses themselves are natural constants that cannot be represented by other constants of nature, or that – as shown in this paper – they can be perfectly well represented by five other fundamental constants, in addition to a time-variable parameter.

**Category:** Mathematical Physics

[127] **viXra:1301.0082 [pdf]**
*submitted on 2013-01-14 09:26:09*

**Authors:** Martin Erik Horn

**Comments:** 8 Pages.

It is a historical accident that we describe Pauli matrices as (2 x 2) matrices and Dirac matrices as (4 x 4) matrices. As it will be shown in this paper we can use (3 x 3) matrices or (9 x 9) matrices for this purpose as well. This hopefully will enable us one day to construct a unified geometric algebra picture which includes Gell-Mann matrices in an appropriate manner.

**Category:** Mathematical Physics

[126] **viXra:1301.0078 [pdf]**
*submitted on 2013-01-14 04:30:47*

**Authors:** Jose Javier garcia Moreta

**Comments:** 10 Pages.

ABSTRACT: We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function.
In this paper and for simplicity we use units so
• Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential.

**Category:** Mathematical Physics

[125] **viXra:1301.0076 [pdf]**
*submitted on 2013-01-14 03:05:17*

**Authors:** S. Kamenshchikov

**Comments:** 12 Pages. contact e-mail: kamphys@gmail.com. Author is looking for postdoc position.

The purpose of this work was to introduce strict, comprehensive definition of perfect chaos, to find out its basic properties in terms of phase transitions and give connections for uncertainties, lying in base of perfect chaos concept. Concept of perfect chaos as undetermined description was introduced basing on two formalized necessary and sufficient conditions: finite phase space resolution and instability of phase space trajectories. Properties of Kolmogorov system, including phase mixing, turned out to be consequences of chaotic state but not its comprehensive and sufficient conditions. Description relativity was defined as mandatory property of perfect chaos – the same areas of phase space may show regular and chaotic properties depending on description space - time accuracy. Herewith evolution of physical system in given generalized phase space can be represented by consequence of regular states and intermediate transitions. For chaotic state with uniform diffusion it was found out that nonlinear dispersion law is mandatory property. One in its turn necessarily leads to space – time instability of probability density and appearance of probability cavities in phase space - phase space attractors where particles density grows up. Case of chaotic state with fixed boundary
and diffusion was considered. It turned out that Fourier decomposition allows to derive relations between coordinate – momentum and time - energy definition uncertainties. It was shown that chaos diffusion factor is the only parameter, limiting product of corresponding uncertainties.

**Category:** Mathematical Physics

[124] **viXra:1301.0065 [pdf]**
*submitted on 2013-01-12 06:19:36*

**Authors:** Dan Visser

**Comments:** 6 Pages.

I present the mathematics of a new ‘Dark Energy Force’ in replay with my former ‘papers’. The reason is particles that feel small gravity, and anti-particles that maybe feel anti-gravity, and the particle-cosmology I use, with negative mass, never have been exposed experimentally to General Relativity, in order to prove that a real anti-gravity exists. However, the mathematics in my frame work theoretically prove, that only dark matter-mass could have negative mass. This is in contradiction with a new theory of Entropy-Gravity, which theoretically proved gravity is not fundamental, but caused by entropy. My framework is also in contradiction with the Elementary Process theory, which also predicts gravity is not fundamental, but will cause anti-gravity by anti-matter with positive mass. Both these frameworks consider their theory in a Big Bang cosmology. So I replayed my mathematics to highlight again, that a new dark matter-force, embedded in a new cosmology named Double Torus Universe, is the only one that could cause real anti-gravity. My framework is independently developed from institutions and based on two extra-time arrows from below the Planck-scale. Additionally, and for the first time, I used a Feynman-diagram to express this dark matter-force in order to illustrate the existence of real anti-gravity theoretically.

**Category:** Mathematical Physics

[123] **viXra:1301.0040 [pdf]**
*submitted on 2013-01-08 00:47:32*

**Authors:** Rodney Bartlett

**Comments:** 5 Pages.

Over 30 years of thinking, plus the insights and mistakes in my viXra articles, reveal the basic blueprint for making this universe. This article continues from where previous articles finished (throughout, I’ve provided links to prior contributions). I begin with explanation of quantum particles, forces and spin in terms of positioning of Mobius loops and the flow of the loops’ binary digits accounting for the interference between gravitation and electromagnetism – together with a link supporting the idea of an electronics-based universe and addressing the topics of hidden variables, quantum fluctuation and virtual particles. The next link speaks of the inverse-square law and infinity. I give Dr. Carl Sagan credit where credit is due - and conclude that, being years ahead of his time, he saw a fundamental truth about the universe’s nature which he decided to include in his book “Contact”. Then time travel into the past (via matrices and the figure-8 Klein bottle), before putting it all together and indulging in some speculation about how to make this universe we’re living in.
I think it’s too simple to say “We don’t need to make the universe … it’s already here”. That statement relies on time being strictly linear (like a straight line, rectilinear). We know it isn’t, but is curvilinear and warped. It’s better to say the universe is here now because our future civilization did the following in the past –

**Category:** Mathematical Physics

[122] **viXra:1212.0167 [pdf]**
*submitted on 2012-12-31 09:45:17*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 8 Pages.

The inherently homogeneous stationary-state and time-dependent Schroedinger equations are often recast into inhomogeneous form in order to resolve their solution nonuniqueness. The inhomogeneous term can impose an initial
condition or, for scattering, the preferred permitted asymptotic behavior. For bound states it provides sufficient focus to exclude all but one of the homogeneous version's solutions. Because of their unique solutions, such inhomogeneous versions of Schroedinger equations have long been the indispensable basis for a solution scheme of successive perturbational corrections which are anchored by their inhomogeneous term. Here it is noted that every such perturbational solution scheme for an inhomogeneous linear vector equation spins off a
nonperturbational continued-fraction scheme. Unlike its representation-independent antecedent, the spin-off scheme only works in representations where all components of the equation's inhomogeneous term are nonzero. But that requirement seems to confer theoretical physics robustness heretofore unknown: for quantum fields the order of the perturbation places a bound on unperturbed particle number, the spin-off scheme contrariwise has only basis elements of unbounded unperturbed particle number. It furthermore is
difficult to visualize such a continued-fraction spin-off scheme generating infinities, since its successive iterations always go into denominators.

**Category:** Mathematical Physics

[121] **viXra:1212.0164 [pdf]**
*submitted on 2012-12-31 04:19:39*

**Authors:** Nicola D'Alfonso

**Comments:** 4 Pages.

In this paper, I introduce a particular discrete spacetime that should
be seriously considered as part of physics because it allows to explain the
characteristics of the motion properly, contrary to what happens with the
continuous spacetime of the common conception.

**Category:** Mathematical Physics

[120] **viXra:1212.0159 [pdf]**
*submitted on 2012-12-29 08:34:36*

**Authors:** Dan Visser

**Comments:** 4 Pages.

This article summarizes theoretical based evidence related to practice for the prediction the universe is not originated from a Big Bang. Instead cosmology could be based on a Double Torus Universe, as is published in my papers in the Vixra-archive. In a few website-articles I also express my vision on the revision of physics and cosmology within this framework. This paper in particular highlights how Gravity could violate General Relativity by a (new) dark energy force in the new Cosmology. This framework contains the connection of the Newton-Gravity force for tiny matter-particles to a dark matter force, producing “+” and “–“ mass-generation, both at scales of about 10^-22 meter. This can cause repulsive gravity in nature. This can open-up a new energy-source for travelling through space by non-relativistic scaling.

**Category:** Mathematical Physics

[119] **viXra:1212.0147 [pdf]**
*submitted on 2012-12-25 15:49:22*

**Authors:** Zafar Turakulov

**Comments:** 9 Pages. no comments

The study of magnetic fields produced by steady currents is a full-valued physical theory which like any other physical theory employs a certain mathematics. This theory has two limiting cases in which source of the field is confined on a surface or a curve. It turns out that mathematical methods to be used in these cases are completely different and differ from from that of the main of the main part of this theory, so, magnetostatics actually consists of three distinct theories. In this work, these three theories are discussed with special attention to the case current carried by a curve. In this case the source serves as a model of thin wire carrying direct current, therefore this theory can be termed magnetostatics of thin wires. The only mathematical method used in this theory till now, is the method of Green's functions. Critical analysis of this method completed in this work, shows that application of this method to the equation for vector potential of a given current density has no foundation and application of this method yields erroneous results

**Category:** Mathematical Physics

[118] **viXra:1212.0128 [pdf]**
*submitted on 2012-12-21 00:50:41*

**Authors:** Steven Kenneth Kauffmann

**Comments:** 5 Pages.

It has recently been shown that self-gravitation reduces static spherically-symmetric cumulative energy distributions below the value of their radii times the "Planck force", which is the inverse of G times the fourth power of c. In this article quantitative treatment of self-gravitation is extended to any static energy density that is nonnegative, smooth and globally
integrable. The resulting dimensionless local gravitational energy-reduction factor (namely the inverse of the local gravitational time-dilation factor) is shown to satisfy the zero-momentum nonrelativistic Lippmann-Schwinger quantum scattering equation for a repulsive potential which is proportional (with a known coefficient) to that static energy density. Standard perturbative Born-type iteration of Lippmann-Schwinger equations can diverge for sufficiently strong potentials, which in the gravitational case correspond to sufficiently large static energy densities. We have been able, however, to
devise an alternate, completely nonperturbative iteration method for Lippmann-Schwinger equations in coordinate representation. Every one of this
nonperturbative method's successive approximations to the local gravitational energy-reduction factor turns out to be positive and less than or equal to unity. In consequence, the self-gravitationally corrected static energy contained in any sphere is bounded by that sphere's diameter times the "Planck force".

**Category:** Mathematical Physics

[117] **viXra:1212.0068 [pdf]**
*submitted on 2012-12-10 05:06:49*

**Authors:** Otto G. Piringer

**Comments:** 12 Pages

Recent publications discussed a possible change with time of Sommerfeld's fine structure constant alpha, in which several of the fundamental constants of Nature are combined. The problem of a changing nature of alpha raises the question whether its value is ultimately a result of chance or reveals an objective law of nature. If the value of alpha is independent of human reason, a derivation of it may be possible from basic numbers, like e and pi, which appear in the logical development of mathematics[1]. In the following investigation a pure mathematical derivation of the fine structure constant is described, starting from a fundamental property of natural numbers. The constant alpha results as a limit value in an algorithm with exponential structures.

**Category:** Mathematical Physics

[116] **viXra:1211.0143 [pdf]**
*submitted on 2012-11-25 05:08:12*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 5 Pages.

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We study also how we could use the WKB
method to recover the potential from the Eigenvalue Staircase for the Riemann

**Category:** Mathematical Physics

[115] **viXra:1211.0140 [pdf]**
*submitted on 2012-11-24 02:12:29*

**Authors:** Guowu Meng

**Comments:** 13 Pages.

Let ${\mathbb R}^{2k+1}_*={\mathbb R}^{2k+1}\setminus\{\vec 0\}$ ($k\ge 1$) and $\pi$: ${\mathbb R}^{2k+1}_*\to \mathrm{S}^{2k}$ be the map sending $\vec r\in {\mathbb R}^{2k+1}_*$ to ${\vec r\over |\vec r|}\in \mathrm{S}^{2k}$. Denote by $P\to {\mathbb R}^{2k+1}_*$ the pullback by $\pi$ of the canonical principal $\mathrm{SO}(2k)$-bundle $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $. Let $E_\sharp\to {\mathbb R}^{2k+1}_*$ be the associated co-adjoint bundle and $E^\sharp\to T^*{\mathbb R}^{2k+1}_*$ be the pullback bundle under projection map $T^*{\mathbb R}^{2k+1}_*\to {\mathbb R}^{2k+1}_*$. The canonical connection on $\mathrm{SO}(2k+1)\to \mathrm{S}^{2k} $ turns $E^\sharp$ into a Poisson manifold.
The main result here is that the real Lie algebra $\mathfrak{so}(2, 2k+2)$ can be realized as a Lie subalgebra of the Poisson algebra $(C^\infty(\mathcal O^\sharp), \{, \})$, where $\mathcal O^\sharp$ is a symplectic leave of $E^\sharp$ of special kind. Consequently, in view of the earlier result of the author, an extension of the classical MICZ Kepler problems to dimension $2k+1$ is obtained. The hamiltonian, the angular momentum, the Lenz vector and the equation of motion for this extension are all explicitly worked out.

**Category:** Mathematical Physics

[114] **viXra:1211.0048 [pdf]**
*submitted on 2012-11-10 00:53:16*

**Authors:** Jian-zhong Zhao

**Comments:** 10 Pages.

Violating the law of energy conservation, Zanaboni Theorem is invalid and Zanaboni's proof is wrong. Zanaboni's mistake of " proof " is analyzed. Energy Theorem for Zanaboni Problem is suggested and proved. Equations and conditions are established in this paper for Zanaboni Problem, which are consistent with , equivalent or identical to each other. Zanaboni Theorem is, for its invalidity , not a mathematical formulation or
proof of Saint-Venant's Principle.
AMS Subject Classifications: 74-02, 74G50

**Category:** Mathematical Physics

[113] **viXra:1210.0132 [pdf]**
*submitted on 2012-10-23 14:58:23*

**Authors:** Ali R. Hadjesfandiari

**Comments:** 8 pages, 1 figure

It is simply proved that the Hamiltonian for an electric point charge interacting with a fixed magnetic monopole does not exist. This shows that the concept of magnetic monopole is inconsistent within the theory of electrodynamics.

**Category:** Mathematical Physics

[112] **viXra:1210.0123 [pdf]**
*submitted on 2012-10-22 15:46:18*

**Authors:** John A. Gowan

**Comments:** 4 Pages.

In the mathematical terms of Evariste Galois' "Group Theory", the "Tetrahedron Model" is a description of the symmetry group of light, including its destruction by asymmetric weak force decays (producing our matter-only Cosmos), and its on-going restoration in obedience to Noether's Theorem of symmetry conservation (as in the conversion of bound to free energy in stars).
The usual symmetry group identified with light is that of local phase transformations, and it is designated as either SO(2) or U(1). However, I am suggesting here that light contains a very much larger (and more interesting) symmetry group associated with its transformation into particle-antiparticle pairs (and back again into light). I don't know what the formal designation of this group might be.
For an expert's explanation of the formal aspects of symmetry and group theory, See: Keith Devlin The Language of Mathematics Chapt. 5 "The Mathematics of Beauty", 1998 W. H. Freeman & Co. (Holt Paperbacks); see also: Ian Stewart Why Beauty is Truth Chapt. 13 "The Five Dimensional Man", Basic Books 2007.

**Category:** Mathematical Physics

[111] **viXra:1210.0114 [pdf]**
*submitted on 2012-10-21 15:02:39*

**Authors:** Jose Miguel Hernandez Perez

**Comments:** 4 Pages. sorry for the grammatical errors

this text can explain where it all started

**Category:** Mathematical Physics

[110] **viXra:1209.0097 [pdf]**
*submitted on 2012-09-27 05:05:24*

**Authors:** Jerzy Hanckowiak

**Comments:** 15 Pages.

Constraints imposed directly on accelerations of the system leading to the relation of constants of motion with appropriate local projectors occurring in the derived equations are considered. In this way a generalization of the Noether's theorem is obtained and constraints are also considered in the phase space.

**Category:** Mathematical Physics

[109] **viXra:1209.0081 [pdf]**
*submitted on 2012-09-24 09:00:38*

**Authors:** Markos Georgallides

**Comments:** 12 Pages.

This article explains how Geometry and geometrical constructions , [ Spaces , Anti-Spaces , Sub-Spaces ] are able to connect Properties , such as Mass , Energy , and the conservation laws of Physics with only one substance , that of Vector ds , which is ds = AB > 0 → < ∞ with Impulses P A + P B = 0 or ≠ 0 at edge points A , B . Since neutrinos may travel faster than light and also gravity instantly affects , a new explanation is needed . The present
article < The Higgs Boson ( Particle ) and the Euclidean Geometry > describes the motion of one of the infinite Sub-Spaces in [ PNS ] , which are moving in Primary Neutral Space . It has been shown that ,
1.. Primary point A , having not Position and consequently not any Space existing , therefore is the only Space , and to exist at a second point B somewhere else , point A must move at point B , where then A ≡ B . Point B is the Primary Anti-Space which Equilibrium point A [ PNS ] = [ A ≡ B ] . Since Primary point A is the only Space , then on it exists Principle of Virtual Displacements W = ∫ P.ds = 0 , or [ ds . ( PA + P B ) = 0 ] , i.e. for any ds > 0 Impulse P = ( PA + P B ) = 0 . All points may exist with P = 0 → ( PNS ) and also with P ≠ 0 , [ P A + P B = 0 for points in Spaces and Anti - Spaces ] , therefore [ PNS ] is self created , and because at each point may exist also P ≠ 0 , then [ PNS ] is a Field with infinite points which have a ± Charge with P = 0 → P → ∞ . Primary Neutral - Space [ PNS ] exists with the infinite Points N with three Spatial dimensions ( Xo , Yo , Zo ) and the infinite Impulses P , ( P xi , Pyi , Pzi ) , and i = 0 → ∞ .
2.. Since points A , B of [ PNS ] coincide with the infinite Points , of the infinite Spaces , Anti-Spaces and Sub-Spaces of [ PNS] , and since Motion may occur at all Bounded Sub-Spaces , then this Relative motion is happening between all points belonging to [ PNS ] and to those points belonging to the other Sub-Spaces ( A ≡ B ) . The Infinite points in [ PNS ] form infinite Units AiBi = ds , which equilibrium by Primary Anti – Space by an Inner Impulse ( P ) at edges A , B where PiA + Pi B ≠ 0 , and ds = 0 → N = ∞ .
3 .. Monads = Quantum = ds = AB / ( n = ∞ → 0 ) = [ a ± b.i ] = 0 → ∞ create Spaces ( S ) , Anti -Spaces ( A-S ) , and Sub-Spaces ( S-S ) of AB , which Sub-Spaces are Bounded Spaces , Anti-Spaces and Sub Spaces in it , and are not purely spatial because are Complex numbers which exist for all Spaces , since binomial dsⁿ is Complex number also .
4.. Monads ds ( dipole AB ) and according to their position in S , A-S , S-S , make the four types of matter , and the Combination of the four types of matter , creates all gauge magnitudes which is Mass and Energy , and so all types of Particles and Fields in universe .The 15 possible types of matter correspond to the , Visible , Invisible , Real and Imaginary Universes ( Visible and Invisible Dark matter and Energy ) . Dipole AB is composed of the two Elements → the [ Dipole AB = matter ≡ is the communicator] , and the Impulse [ P ] with the Bounded Impulses ( PA , P B ) .
5.. The difference of Impulses dP = P B – PA > = < 0 of Dipole AB (mass) , creates ± charge . For very small ds ( near zero) which happens at the boundaries of Spaces , ± charge may be point charge ( Spaces form open Strings while Sub-Spaces form closed Strings . Cosmic rays is a Quantum field from a , near zero ds Sub-Space ) , and in very large scales ds ,
is of ± charge and of the same Field , ( This because Particles , wave like , do not enter a Space smaller than their wavelength ) .
6.. A ray , say M - Ray , interact on the infinite Monads of [PNS] with infinite velocity and zero frequency . This Motion is Continuous and occurs on Dimensional Bounded Units , ds , and not on Points ( this happens only for very small ds near zero and at boundaries of the Spaces ) which are dimensionless . The difference of Impulse dP = P B-PA on points A , B and on points Pi A , Pi B is ± charge . All particles act as wave ( wave-particle duality ) because of the Total energy conservation law of Pythagoras in 2,3 Dim .
7.. The four Interaction of particles or Fields occur directly or Indirectly .

**Category:** Mathematical Physics

[108] **viXra:1208.0237 [pdf]**
*submitted on 2012-08-30 04:32:08*

**Authors:** Xiong Wang

**Comments:** 15 Pages.

How to relate the physical \emph{real} reality with the logical \emph{true} abstract mathematics concepts is nothing but pure postulate. The most basic postulates of physics are by using what kind of mathematics to describe the most fundamental concepts of physics. Main point of relativity theories is to remove incorrect and simplify the assumptions about the nature of space-time. There are plentiful bonus of doing so, for example gravity emerges as natural consequence of curvature of spacetime. We argue that the Einstein version of general relativity is not complete, since it can't explain quantum phenomenon. If we want to reconcile quantum, we should give up one implicit assumption we tend to forget: the differentiability. What would be the benefits of these changes? It has many surprising consequences. We show that the weird uncertainty principle and non-commutativity become straightforward in the circumstances of non-differentiable functions. It's just the result of the divergence of usual definition of \emph{velocity}. All weirdness of quantum mechanics are due to we are trying to making sense of nonsense. Finally, we proposed a complete relativity theory in which the spacetime are non-differentiable manifold, and physical law takes the same mathematical form in all coordinate systems, under arbitrary differentiable or non-differentiable coordinate transformations. Quantum phenomenon emerges as natural consequence of non-differentiability of spacetime.

**Category:** Mathematical Physics

[107] **viXra:1208.0071 [pdf]**
*submitted on 2012-08-16 15:43:12*

**Authors:** Laszlo I. Orban

**Comments:** 5 Pages.

Many trials attempted to understand the neutrinos ever since Pauli theoretically concluded its existence from the conservation of energy calculations. The present paper demonstrates that commencing from two appropriately chosen measurement systems, the mass of the electron-neutrino can be calculated from the mass of the electron and the fine-structure constant. The mass of the neutrino can be determined by the theoretically derived expression (m_k=\alpha^3 m_e) (m_k￼ is the mass of the neutrino, m_e is the mass of electron, alpha is the fine-structure constant).

**Category:** Mathematical Physics

[106] **viXra:1208.0048 [pdf]**
*submitted on 2012-08-12 02:37:48*

**Authors:** Xiong Wang

**Comments:** 13 Pages. author name: Xiong WANG Email:wangxiong8686@gmail.com

``To see a World in a Grain of Sand, And a Heaven in a Wild'' We will try to see the development and the whole picture of theoretical physic through the evolution of the very fundamental concept of mass. 1The inertial mass in Newtonian mechanics 2 The Newtonian gravitational mass 3 Mass in Lagrangian formulism 4 Mass in the special theory of relativity 5 $E = MC^2$ 6 Mass in quantum mechanics 7 Principle of equivalence and general relativity 8 The energy momentum tensor in general relativity 9 Mass in the standard model of particle physics 10 The higgs mechanism

**Category:** Mathematical Physics

[105] **viXra:1208.0036 [pdf]**
*submitted on 2012-08-08 17:19:13*

**Authors:** Dan Visser

**Comments:** 7 Pages.

The main issue in this paper is my mathematics to be presented about the maximum of dark energy depending on the information-differences on the wall of any volume in the Double Torus. Secondly the expressions must be worked out further by invitation to them how are triggered by my ideas the universe has a Double Torus geometry. Thirdly I go deeper into details with dark matter, not only stating dark matter is a spatial particle that spins and gets its energy from its acceleration into a dark matter torus, but also pretending dark matter gets its mass from the vacuum energy. I lay out the conditions for understanding why the Big Bang dynamics is therefore a part of the Double Torus and how the dark flow in the universe emerge from the Double Torus dark energy equation. Fourthly I refer to the pretention neutrinos should be sensitive for the flow of dark matter particles expressed in the set of equations in a former paper. But extensively this paper amplifies this theoretical neutrino-evidence, despite all the confusion around the truth of neutrinos-faster-than-light. Fifthly I observe some dark energy and dark matter issues from some of my former papers.

**Category:** Mathematical Physics

[104] **viXra:1207.0059 [pdf]**
*submitted on 2012-07-16 02:49:37*

**Authors:** Xiong Wang

**Comments:** 2 Pages.

Memristor was postulated by Chua in 1971 by analyzing mathematical relations
between pairs of fundamental circuit variables and realized by HP laboratory in 2008. This
relation can be generalized to include any class of two-terminal devices whose properties
depend on the state and history of the system. These are called memristive systems, including
current-voltage for the memristor, charge-voltage for the memcapacitor, and current-flux for the
meminductor. This paper further enlarge the family of elementary circuit elements, in order to
model many irregular and exotic nondifferentiable phenomena which are common and dominant
to the nonlinear dynamics of many biological, molecular and nanodevices.

**Category:** Mathematical Physics

[103] **viXra:1207.0036 [pdf]**
*submitted on 2012-07-11 00:23:09*

**Authors:** Alexander Egoyan

**Comments:** 10 Pages.

In this work a conceptual basis for multidimensional physics (MD physics) is proposed. The new physics is based on the elastic model of multidimensional geometry [1]. Reality may be considered as the process of time evolution of holistic macro objects - elastic membranes. An embedded membrane in this multidimensional world will look different for the external and internal observers: from the outside it will look like a material object with smooth infinitesimal geometry, while from the inside our Universe-like space-time fabric. When interacting with elementary particles and other membranes, a membrane will transform their energy into its elastic energy (a new form of energy) - the energy of stretching of the infinitesimal segments. For example, living organisms play the role of internal observers of the Universe, and at the same time they serve as external observers for 2D membranes embedded into our Universe. A new explanation of gravity and cosmological aspects are also discussed.

**Category:** Mathematical Physics

[102] **viXra:1207.0032 [pdf]**
*submitted on 2012-07-09 04:04:07*

**Authors:** Mourici Shachter

**Comments:** 5 Pages.

This short paper prove that mathematically, Reality is not real . This short paper is not about Heisenberg's uncertainty principle of quantum physics. There is another uncertainty principle that depends solely on mathematical arguments and explains why our world can't be easily equated. Or more accurately can be describe in infinitely different ways all of those representations are mathematically correct. Which mean that the representation of any physical phenomena is not unique.
. Given an example how to use it to solve complicate problems in engineering

**Category:** Mathematical Physics

[101] **viXra:1206.0078 [pdf]**
*submitted on 2012-06-22 02:10:33*

**Authors:** Shachter Mourici

**Comments:** 23 Pages.

In this paper an entirely new approach is used to solve the old problem known as "The Unified Theory of Electrical Machines" Instead of solving an electric circuit with time dependent resistors and coils. I spent a lot of time in finding the appropriate coordinate system in which the problem becomes very simple. Instead of mathematical reasoning with innumerous number of mathematical equation I used pictorial reasoning
This Unified Theory of Electrical Machines is the shortest and therefore can be used to teach student the principles of electrical machines in a one semester course
The systematic procedure introduced in this paper is not limited to machine theory and can be applied in many physic and engineering problems.

**Category:** Mathematical Physics

[100] **viXra:1206.0069 [pdf]**
*submitted on 2012-06-19 15:01:49*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 9 Pages.

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function
• Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula ,Bolte’s law, Quantum chaos.

**Category:** Mathematical Physics

[99] **viXra:1206.0066 [pdf]**
*submitted on 2012-06-19 05:22:29*

**Authors:** Mourici Shachter

**Comments:** 16 Pages.

It is well known that physics explains natural phenomena using mathematics, But what happens if we derive from a good physical experiment a wrong mathematical equation, use it for more than 100 years without knowing it is wrong. In this paper I develop again the equation of energy conversion in a general electrical machine and prove that the equations we use are wrong. One of Professor Einstein statements was that the laws of physics are the same for every observer so I made the electrical equation of the machine to look like the mechanical equation. What I found was astonishing and is valid for all other area in physics. It is found that in general any constant in physic can be represented by a superposition of time and phase dependent sinusoidal function. So may be what we think about speed of light and other physical constant is entirely wrong. In the last part of this issue, I use the consequences of that article to create a virtual universe.

**Category:** Mathematical Physics

[98] **viXra:1206.0049 [pdf]**
*submitted on 2012-06-12 15:23:28*

**Authors:** Thomas J. Buckholtz

**Comments:** 11 Pages.

We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Ratios of theoretical numbers of analogs of various types of particles match observed ratios of densities for baryonic matter, dark matter, and dark energy.

**Category:** Mathematical Physics

[97] **viXra:1206.0028 [pdf]**
*submitted on 2012-06-07 15:07:57*

**Authors:** Dan Visser

**Comments:** 10 Pages.

This paper presents a set of equations, as well as further derivations and calculations, to present dark matter in an alternative cosmology. The alternative is: The Universe did not start with the Big Bang, but is a recalculated Double Torus Universe of dark energy and dark matter. The calculations within this framework show a dark matter-particle, which has the shape of a smallest possible Double Torus, and has a constant diameter of R ≈ 0.712 x 10^-22 [m] at where it exists. At this length the lowest acceleration for Newton gravity becomes a dark matter-acceleration; the Newton force then changes into a lowest dark matter force. This paper shows both forces are embedded in a united ‘new dark energy force’. In the transition of Newton gravity to dark matter gravity, the new dark energy force has a value of 10^-116 kg^4s^2. Accordingly another calculation reveals this force is a ‘force to recalculate space-time itself’. Further calculations also enable to mark dark matter mass with a value of ≈ 2.8 keV/c^2. Again accordingly the dark matter-density (in kg/m) is ≈ 71 gram per 1 million-km (≈1/149 the distance to the sun, or more than three times the distance from Earth to Moon). The dark energy force uses extra time-arrows from an under-laying time-domain of conventional space-time’. This directly gives evidence to the perception gravity is not fundamental. In general this paper relates dark matter mass, new dark energy force and the level where Newton gravity and dark matter meet each other; specifically in that level space-time is recalculated. Moreover an alternative perception of the Higgs-field is given, related to this recalculation.

**Category:** Mathematical Physics

[96] **viXra:1206.0026 [pdf]**
*submitted on 2012-06-07 08:44:08*

**Authors:** Jerzy Hanckowiak

**Comments:** 24 Pages.

A new interpretation of the basic vector of the free Fock space (FFS) and the FFS is proposed. The approximations to various equations with additional parameters, for n-point information (n-pi), are also considered in the case of non-polynomial nonlinearities.
Key words: basic, generating and state vectors, local and global, Cuntz relations, perturbation and closure principles, homotopy analysis method, Axiom of Choice, consilience.

**Category:** Mathematical Physics

[95] **viXra:1206.0021 [pdf]**
*submitted on 2012-06-06 08:33:46*

**Authors:** Xiong Wang

**Comments:** 8 Pages.

A new simple and compact approach to hydrodynamic is presented using
the formalism of geometric algebra (GA).

**Category:** Mathematical Physics

[94] **viXra:1205.0102 [pdf]**
*submitted on 2012-05-25 22:01:25*

**Authors:** Jian-zhong Zhao

**Comments:** 16 Pages.

The problem of a cylinder with a small spherical cavity loaded by an
equilibrium system of forces is suggested and discussed and its formulation of Saint-Venant's Principle is established. It is evident that finding
solutions of boundary-value problems is a precise and pertinent approach
to establish Saint-Venant type decay of elastic problems.
Keywords : Saint-Venant’s Principe, proof, provability, solution, decay, formulation,
cavity
AMS Subject Classifications: 74-02, 74G50

**Category:** Mathematical Physics

[93] **viXra:1205.0089 [pdf]**
*submitted on 2012-05-22 21:05:18*

**Authors:** Jian-zhong Zhao

**Comments:** 9 Pages.

The Statement of Modified Saint-Venant's Principle is suggested. The
axisymmetrical deformation of the infinite circular cylinder loaded by an
equilibrium system of forces on its near end is discussed and its formulation of Modified Saint-Venant's Principle is established. It is evident that
finding solutions of boundary-value problems is a precise and pertinent
approach to establish Saint-Venant type decay of elastic problems.
AMS Subject Classifications: 74-02, 74G50

**Category:** Mathematical Physics

[92] **viXra:1205.0017 [pdf]**
*submitted on 2012-05-03 17:23:45*

**Authors:** editor Florentin Smarandache

**Comments:** 92 Pages.

Neutrosophic Physics.
Let be a physical entity (i.e. concept, notion, object, space, field, idea, law, property, state, attribute, theorem, theory, etc.),

**Category:**

[91] **viXra:1205.0010 [pdf]**
*submitted on 2012-05-03 09:04:50*

**Authors:** Blaise Mouttet

**Comments:** 6 Pages.

It has been erroneously asserted by the circuit theorist Leon Chua that all zero-crossing pinched hysteresis curves define memristors. This claim has been used by Stan Williams of HPLabs to assert that all forms of RRAM and phase change memory are memristors. This paper demonstrates several examples of dynamic systems which fall outside of the constraints of memristive systems and yet also produce the same type of zero-crossing hysteresis curves claimed as a fingerprint for a memristor. This establishes that zero-crossing hysteresis serves as insufficient evidence for a memristor.
Keywords- non-linear dynamic systems, memresistor, phase change memory, RRAM, ReRAM

**Category:** Mathematical Physics

[90] **viXra:1205.0009 [pdf]**
*submitted on 2012-05-03 09:13:44*

**Authors:** Blaise Mouttet

**Comments:** 2 Pages.

This is a short response to a recent paper by Kim et al. [1] which correctly notes that the zero-crossing pinched hysteresis loop of a memristor or memristive system must hold for all amplitudes, for all frequencies, and for all initial conditions, of any periodic testing waveform, such as sinusoidal or triangular signals, which assumes both positive and negative values over each period of the waveform. An example is noted from the literature indicating that TiO2 memory resistors might not be considered either memristors or memristive systems given this constraint.
Keywords- non-linear dynamic systems, memresistor, RRAM, ReRAM

**Category:** Mathematical Physics

[89] **viXra:1205.0008 [pdf]**
*submitted on 2012-05-03 09:22:18*

**Authors:** Blaise Mouttet

**Comments:** 5 Pages.

It has been claimed that pinched hysteresis curves are the fingerprint of memristors. This paper demonstrates that a linear resistor in parallel with a nonlinear, square law capacitor also produces pinched hysteresis curves. Spice simulations are performed examining the current vs. voltage behavior of this circuitry under different amplitudes and frequencies of an input signal. Based on this finding a more generalized dynamic systems model is suggested for ReRAM and neuromorphic modeling to cover a broader range of pinched hysteresis curves.
Keywords- non-linear circuit theory, RRAM, ReRAM, memristor, memristive systems, memadmittance systems, memresistor

**Category:** Mathematical Physics

[88] **viXra:1204.0094 [pdf]**
*submitted on 2012-04-27 06:21:14*

**Authors:** Etkin V.A.

**Comments:** 9 Pages. English

It is shown, that change of image of heat and work in open systems
entails necessity to revise of conditions of material equilibrium, found
by Gibbs. Thus the chemical potential gives way to other potentials in
conformity with conditions of unambiguity of researched processes.

**Category:** Mathematical Physics

[87] **viXra:1204.0051 [pdf]**
*submitted on 2012-04-14 12:23:30*

**Authors:** sangwha Yi

**Comments:** 11 Pages. Thank you.

In the general relativity theory, in the Rindler’s coordinate theory, find the present accelerated theory’s problem, resurface Rindler’s coordinate theory that used the tetrad on the new method.The theory’s concept is that save Rindler’s coordinate transformation in the other way.

**Category:** Mathematical Physics

[86] **viXra:1204.0043 [pdf]**
*submitted on 2012-04-11 11:01:42*

**Authors:** Dan Visser

**Comments:** 10 Pages.

Neutrinos-faster-than-light? The science-battle is not yet over! ‘Yes’, said the OPERA-team in September 22 2011. ‘No’, said the ICARUS-team in February 23 2012. But this paper carries on that it is undoubtedly correct that neutrinos can go faster-than-light. Neutrinos can only do that in neutrino-pairs: I call these pairs Duonistic Neutrinos! This paper presents the set of equations to prove that. The smallest gravity-acceleration g’ appears to be prior to the trajectory of single packaged neutrinos. OPERA and ICARUS might be right both in the end.

**Category:** Mathematical Physics

[85] **viXra:1203.0089 [pdf]**
*submitted on 2012-03-24 11:31:41*

**Authors:** Elemer E Rosinger

**Comments:** 13 Pages.

It appears not to be known that subjecting the axioms to certain conditions, such as for instance to be physically meaningful, may interfere with the logical essence of axiomatic systems, and do so in unforeseen ways, ways that should be carefully considered and accounted for.
Consequently, the use of "physical intuition" in building up axiomatic systems for various theories of Physics may lead to situations which
have so far not been carefully considered.

**Category:** Mathematical Physics

[84] **viXra:1203.0087 [pdf]**
*submitted on 2012-03-22 09:37:31*

**Authors:** Elemer E Rosinger

**Comments:** 16 Pages.

This paper presents the phenomenon of disconnect in the axiomatic approach to theories of Physics, a phenomenon which appears due to the insistence on axioms which have a physical meaning. This insistence introduces a restriction which is foreign to the abstract nature of axiomatic systems as such. Consequently, it turns out to introduce as well the mentioned disconnect. The axiomatic approach in Physics has a longer tradition. It is there already in Newton's Principia. Recently for instance, a number of axiomatic approaches have been proposed in
the literature related to Quantum Mechanics. Special Relativity, [2], had from its beginning in 1905 been built upon two axioms, namely,
the Galilean Relativity and the Constancy of the Speed of Light in inertial reference frames. Hardly noticed in wider circles, the independence
of these two axioms had quite early been subjected to scrutiny, [5,3], and that issue has on occasion been addressed ever since, see
[8,4,24] and the literature cited there. Recently, [24], related to these two axioms in Special Relativity, the following phenomenon of wider importance in Physics was noted. As the example of axiomatization of Special Relativity shows it, it is possible to face a disconnect
between a system of physically meaningful axioms, and on the other hand, one or another of the mathematical models used in the study of the axiomatized physical theory. The consequence is that, seemingly unknown so far, one faces in Physics the possibility that the axiomatic method has deeper, less obvious, and in fact not considered, or simply overlooked limitations. As there is no reason to believe that the system of the usual two axioms of Special Relativity is the only one subjected to such a disconnect, the various foundational ventures in modern Physics, related for instance to gravitation, quanta, or their bringing together in an overarching theory, may benefit from the study of the possible sources and reasons for such a disconnect. An attempt
of such study is presented in this paper.

**Category:** Mathematical Physics

[83] **viXra:1203.0059 [pdf]**
*submitted on 2012-03-16 03:56:23*

**Authors:** Matti Pitkänen

**Comments:** 41 Pages.

A generalization of number concept is proposed. One can replace integer n with n-dimensional Hilbert space and sum + and product × with direct sum ⊕ and tensor product ⊗ and introduce their co-operations, the definition of which is highly non-trivial.

This procedure yields also Hilbert space variants of rationals, algebraic numbers, p-adic number fields, and even complex, quaternionic and octonionic algebraics. Also adeles can be replaced with their Hilbert space counterparts. Even more, one can replace the points of Hilbert spaces with Hilbert spaces and repeat this process, which is very similar to the construction of infinite primes having interpretation in terms of repeated second quantization. This process could be the counterpart for construction of n^{th} order logics and one might speak of Hilbert or quantum mathematics. The construction would also generalize the notion of algebraic holography and provide self-referential cognitive representation of mathematics.

This vision emerged from the connections with generalized Feynman diagrams, braids, and with the hierarchy of Planck constants realized in terms of coverings of the imbedding space. Hilbert space generalization of number concept seems to be extremely well suited for the purposes of TGD. For instance, generalized Feynman diagrams could be identifiable as arithmetic Feynman diagrams describing sequences of arithmetic operations and their co-operations. One could interpret ×_{q} and +_{q} and their co-algebra operations as 3-vertices for number theoretical Feynman diagrams describing algebraic identities X=Y having natural interpretation in zero energy ontology. The two vertices have direct counterparts as two kinds of basic topological vertices in quantum TGD (stringy vertices and vertices of Feynman diagrams). The definition of co-operations would characterize quantum dynamics. Physical states would correspond to the Hilbert space states assignable to numbers. One prediction is that all loops can be eliminated from generalized Feynman diagrams and diagrams are in projective sense invariant under permutations of incoming (outgoing legs).

**Category:** Mathematical Physics

[82] **viXra:1203.0058 [pdf]**
*submitted on 2012-03-16 03:58:04*

**Authors:** Matti Pitkänen

**Comments:** 18 Pages.

Absolute Galois Group defined as Galois group of algebraic numbers regarded as extension of rationals is very difficult concept to define. The goal of classical Langlands program is to understand the Galois group of algebraic numbers as algebraic extension of rationals - Absolute Galois Group (AGG) - through its representations. Invertible adeles -ideles - define Gl_{1} which can be shown to be isomorphic with the Galois group of maximal Abelian extension of rationals (MAGG) and the Langlands conjecture is that the representations for algebraic groups with matrix elements replaced with adeles provide information about AGG and algebraic geometry.

I have asked already earlier whether AGG could act is symmetries of quantum TGD. The basis idea was that AGG could be identified as a permutation group for a braid having infinite number of strands. The notion of quantum adele leads to the interpretation of the analog of Galois group for quantum adeles in terms of permutation groups assignable to finite l braids. One can also assign to infinite primes braid structures and Galois groups have lift to braid groups.

Objects known as dessins d'enfant provide a geometric representation for AGG in terms of action on algebraic Riemann surfaces allowing interpretation also as algebraic surfaces in finite fields. This representation would make sense for algebraic partonic 2-surfaces, and could be important in the intersection of real and p-adic worlds assigned with living matter in TGD inspired quantum biology, and would allow to regard the quantum states of living matter as representations of AGG. Adeles would make these representations very concrete by bringing in cognition represented in terms of p-adics and there is also a generalization to Hilbert adeles.

**Category:** Mathematical Physics

[81] **viXra:1203.0007 [pdf]**
*submitted on 2012-03-03 03:23:21*

**Authors:** Jake Vlastos

**Comments:** 16 Pages.

our universe has 5 dimensions adn this project is the proof for this theory

**Category:** Mathematical Physics

[80] **viXra:1203.0005 [pdf]**
*submitted on 2012-03-02 04:06:06*

**Authors:** Dan Visser

**Comments:** 7 Pages.

The evidence comes from an alternative calculation of deviations in the dipole fine-structure constant (α). The alternative calculation reveals α deviations spatially and timely connected to a curved dark flow that fits a closed-curved and cyclic Double Torus Universe. This opens-up a new perception the Big Bang is spinning inside another cosmological model. In reality this means the deviation in the dipole α represents the recalculation of the electromagnetic force. Hence, in terms of a cosmological completeness, with also the other forces involved, one could say reality is recalculated by new features of the Double Torus Universe. The features are described earlier in papers posted in the Vixra-archive. Specifically this paper gives the derivations and calculations to show the evidence α deviations are spatially and timely connected in the Double Torus Universe.

**Category:** Mathematical Physics

[79] **viXra:1202.0075 [pdf]**
*submitted on 2012-02-25 01:52:59*

**Authors:** Elemer E Rosinger

**Comments:** 29 Pages.

Information being a relatively new concept in science, the likelihood is pointed out that we do not yet have a good enough grasp of its nature and relevance. This likelihood is further enhanced by the ubiquitous use of information which creates the perception of a manifest, yet in fact, rather superficial familiarity. The paper suggests several aspects which may be essential features of information, or on the contrary, may not be so. In this regard, further studies are obviously needed, studies which may have to avoid with care various temptations to reductionism, like for instance the one claiming that ``information is physical".

**Category:** Mathematical Physics

[78] **viXra:1202.0001 [pdf]**
*submitted on 2012-02-01 02:19:14*

**Authors:** Victor Katyushchik

**Comments:** 4 Pages.

The three-dimensional space formatting allows to operate on infinitely large and infinitely small quantities confidently, without any contradictions, paradoxes and uncertainties.

**Category:** Mathematical Physics

[77] **viXra:1201.0119 [pdf]**
*submitted on 2012-01-30 04:01:12*

**Authors:** Prakhar bhatnagar

**Comments:** 5 Pages.

Magnetic monopole is a hypothetical particle with a single pole. In this paper a new mathematical structure for Dirac string has been proposed .Quantitative aspects and qualitative aspects of a monopole represented as a Dirac string have been highlighted. Magnetic bundle has been defined in a complex form and pole has been defined as composition of that bundle for single pole the pole variable is single. The pole can be considered as a group of threads or a point lying on a monopole magnet bundle for one pole the thread is single and one dimensional. The function is in complex form and defines magnetic bundle.

**Category:** Mathematical Physics

[76] **viXra:1201.0117 [pdf]**
*submitted on 2012-01-29 07:51:38*

**Authors:** Dan Visser

**Comments:** 10 Pages.

This paper describes what New Dark Energy is, as well as my comment “Nobel Nominations in a New World” to the Nobel Committee. These seemingly different looking subjects are importantly connected in a plead to change the way Nobel-nominations are performed in a changing world with internet and alternative archives, such as viXra. The point is, that institutional established physics and cosmology block new ideas from the public domain. Therefore an appendix has been added to this paper to summarize in a nutshell, relativity, space-expansion, accelerated space-expansion and the one time-direction in the Big Bang Cosmology, in order to explain better what new dark energy is and what its meaning is for physics and new cosmology. That message is meant for the Nobel Committee. Furthermore three-why’s are answered: Why are two extra time-directions needed in a new cosmology? Why is the introduction of dark mass, squared? Why would there be a Double Torus for New Cosmology? Also the basic-formulas are summarized, referring to my papers, such as the dark energy force formula from my thought-experiment, followed by its transformed-version: the force smaller than the smallest gravity. In the end New Dark Energy is formulated as a product of new dark mass (squared) and two extra time-directions from below the Planck scale. This marks that New Dark Energy could recalculate the established dual unitary-entangled quantum-spaces faster backwards in time than time goes forward in the Big Bang Cosmology ! This affects the established quantum dynamics and classical reality towards the past and future differently than Einstein’s General Relativity is prescribing. The letter to the Nobel Committee is send by me, because no other institutions is doing that for me.

**Category:** Mathematical Physics

[75] **viXra:1201.0065 [pdf]**
*submitted on 2012-01-16 10:48:52*

**Authors:** Florentin Smarandache

**Comments:** 4 Pages.

In a similar way as passing from Euclidean Geometry to Non-Euclidean Geometry, we
can pass from Subluminal Physics to Superluminal Physics, and further to Instantaneous Physics.
In the lights of two consecutive successful CERN experiments with superluminal particles in the
Fall of 2011, we believe that these two new fields of research should begin developing.

**Category:** Mathematical Physics

[74] **viXra:1112.0094 [pdf]**
*submitted on 2011-12-31 14:02:34*

**Authors:** DT Froedge

**Comments:** 12 Pages.

This paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.

**Category:** Mathematical Physics

[73] **viXra:1112.0055 [pdf]**
*submitted on 2011-12-18 14:01:31*

**Authors:** Dan Visser

**Comments:** 4 Pages. Avalable only for arXiv and informing me by email.

In this paper I give a formulation for why a new Higgs-mass is considered otherwise than is usually done. This leads to an additional explanation of my earlier posted papers about neutrinos-faster-than-light-in-vacuum; I also refer to my earlier calculated new Higgs-mass. The addition is a deeper analysis, which does not change the result in the former paper. It is extending the Higgs-energy. The first prediction is the Higgs-particle is a Limited Boson-Surface, or Higgs-LBS. This means: It is not a singular Higgs-mass boson. The second prediction is: The occurrence of an Higgs-LBS may be about 60 nanoseconds before a proton-proton collision in an accelerator, such as the LHC in CERN. This is possible because the Higgs-energy is related to a new dark energy force squared. These predictions are supposed to fit in a new cosmological hypothesis, called the Double Torus of dark energy and dark matter, wherein a new dark energy force is defined as a force smaller than the smallest gravity, which could act beyond General Relativity.

**Category:** Mathematical Physics

[72] **viXra:1111.0106 [pdf]**
*submitted on 28 Nov 2011*

**Authors:** Dan Visser

**Comments:** 7 Pages.

In the formulations of this 'paper' speaks the existence of a force smaller than the smallest gravity.
This is a new dark energy force, which affects neutrinos differently than is assumed according to current
physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. The 'paper'
is also is an overview of recent 'papers' [1] , which already described these issues, but a deeper
analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on
these issues are the falsification for my formulations, but until now my formulations withstand several
experimental results, and in this case the match with the latest neutrino-faster-than-light experiments
is very convincing (more attention might be given to this 'paper' towards institutional disciplines by
the Arxiv or Nature).

**Category:** Mathematical Physics

[71] **viXra:1111.0091 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 24 pages.

The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following.

- Zero energy ontology (ZEO) and the related notion of causal diamond CD (CD is short hand for the cartesian product of causal diamond of M
^{4}and of CP_{2}). ZEO leads to the notion of partonic 2-surfaces at the light-like boundaries of CD and to the notion of string world sheet. These notions are central in the recent view about TGD. One can assign to the partonic 2-surfaces a conformal moduli space having as additional coordinates the positions of braid strand ends (punctures). By electric-magnetic duality this moduli space must correspond closely to the moduli space of string world sheets. - Electric-magnetic duality realized in terms of string world sheets and partonic 2-surfaces. The group G and its Langlands dual
^{L}G would correspond to the time-like and space-like braidings. Duality predicts that the moduli space of string world sheets is very closely related to that for the partonic 2-surfaces. The strong form of 4-D general coordinate invariance implying electric-magnetic duality and S-duality as well as strong form of holography indeed predicts that the collection of string world sheets is fixed once the collection of partonic 2-surfaces at light-like boundaries of CD and its sub-CDs is known. - The proposal is that finite measurement resolution is realized in terms of inclusions of hyperfinite factors of type II
_{1}at quantum level and represented in terms of confining effective gauge group. This effective gauge group could be some associate of G: gauge group, Kac-Moody group or its quantum counterpart, or so called twisted quantum Yangian strongly suggested by twistor considerations. At space-time level the finite measurement resolution would be represented in terms of braids at space-time level which come in two varieties correspond to braids assignable to space-like surfaces at the two light-like boundaries of CD and with light-like 3-surfaces at which the signature of the induced metric changes and which are identified as orbits of partonic 2-surfaces connecting the future and past boundaries of CDs.There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable.

In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD.

- The natural identification of the associate of G is as quantum Yangian of Kac-Moody type group associated with Minkowskian open string model assignable to string world sheet representing a string moving in the moduli space of partonic 2-surface. The dual group corresponds to Euclidian string model with partonic 2-surface representing string orbit in the moduli space of the string world sheets. The Kac-Moody algebra assigned with simply laced G is obtained using the standard tachyonic free field representation obtained as ordered exponentials of Cartan algebra generators identified as transversal parts of M
^{4}coordinates for the braid strands. The importance of the free field representation generalizing to the case of non-simply laced groups in the realization of finite measurement resolution in terms of Kac-Moody algebra cannot be over-emphasized. - Langlands duality involves besides harmonic analysis side also the number theoretic side. Galois groups (collections of them) defined by infinite primes and integers having representation as symplectic flows defining braidings. I have earlier proposed that the hierarchy of these Galois groups define what might be regarded as a non-commutative homology and cohomology. Also G has this kind of representation which explains why the representations of these two kinds of groups are so intimately related. This relationship could be seen as a generalization of the MacKay correspondence between finite subgroups of SU(2) and simply laced Lie groups.
- Symplectic group of the light-cone boundary acting as isometries of the WCW geometry kenociteallb/compl1 allowing to represent projectively both Galois groups and symmetry groups as symplectic flows so that the non-commutative cohomology would have braided representation. This leads to braided counterparts for both Galois group and effective symmetry group.
- The moduli space for Higgs bundle playing central role in the approach of Witten and Kapustin to geometric Landlands program is in TGD framework replaced with the conformal moduli space for partonic 2-surfaces. It is not however possible to speak about Higgs field although moduli defined the analog of Higgs vacuum expectation value. Note that in TGD Universe the most natural assumption is that all Higgs like states are "eaten" by gauge bosons so that also photon and gluons become massive. This mechanism would be very general and mean that massless representations of Poincare group organize to massive ones via the formation of bound states. It might be however possible to see the contribution of p-adic thermodynamics depending on genus as analogous to Higgs contribution since the conformal moduli are analogous to vacuum expectation of Higgs field.

[70] **viXra:1111.0090 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 18 pages.

Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes.

Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization?

- Quantum view about consciousness and cognition leads to a proposal that p-adic physics serves as a correlate for cognition. Together with the notion of infinite primes this suggests that number theory should play a key role in the axiomatics.
- Algebraic geometry allows algebraization of the set theory and this kind of approach suggests itself strongly in physics inspired approach to the foundations of mathematics. This means powerful limitations on the notion of set.
- Finite measurement resolution and finite resolution of cognition could have implications also for the foundations of mathematics and relate directly to the fact that all numerical approaches reduce to an approximation using rationals with a cutoff on the number of binary digits.
- The TGD inspired vision about consciousness implies evolution by quantum jumps meaning that also evolution of mathematics so that no fixed system of axioms can ever catch all the mathematical truths for the simple reason that mathematicians themselves evolve with mathematics.

[69] **viXra:1111.0089 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 79 pages.

In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons.

*1. Infinite primes, Galois groups, algebraic geometry, and TGD*

In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.

Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.

The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.

- What makes infinite primes interesting from the point of view of algebraic geometry is that
infinite primes, integers and rationals at the n:th level of the hierarchy are in 1-1 correspondence with rational functions of n arguments. One can solve the roots of associated polynomials and perform a root decomposition of infinite primes at various levels of the hierarchy and assign to them Galois groups acting as automorphisms of the field extensions of polynomials defined by the roots coming as restrictions of the basic polynomial to planes x
_{n}=0, x_{n}=x_{n-1}=0, etc... - These Galois groups are suggested to define non-commutative generalization of homotopy and homology theories and non-linear boundary operation for which a geometric interpretation in terms of the restriction to lower-dimensional plane is proposed. The Galois group G
_{k}would be analogous to the relative homology group relative to the plane x_{k-1}=0 representing boundary and makes sense for all number fields also geometrically. One can ask whether the invariance of the complex of groups under the permutations of the orders of variables in the reduction process is necessary. Physical interpretation suggests that this is not the case and that all the groups obtained by the permutations are needed for a full description. - The algebraic counterpart of boundary map would map the elements of G
_{k}identified as analog of homotopy group to the commutator group [G_{k-2},G_{k-2}] and therefore to the unit element of the abelianized group defining cohomology group. In order to obtains something analogous to the ordinary homology and cohomology groups one must however replaces Galois groups by their group algebras with values in some field or ring. This allows to define the analogs of homotopy and homology groups as their abelianizations. Cohomotopy, and cohomology would emerge as duals of homotopy and homology in the dual of the group algebra. - That the algebraic representation of the boundary operation is not expected to be unique turns into blessing when on keeps the TGD as almost topological QFT vision as the guide line. One can include all boundary homomorphisms subject to the condition that the anticommutator δ
^{i}_{k}δ^{j}_{k-1}+δ^{j}_{k}δ^{i}_{k-1}maps to the group algebra of the commutator group [G_{k-2},G_{k-2}]. By adding dual generators one obtains what looks like a generalization of anticommutative fermionic algebra and what comes in mind is the spectrum of quantum states of a SUSY algebra spanned by bosonic states realized as group algebra elements and fermionic states realized in terms of homotopy and cohomotopy and in abelianized version in terms of homology and cohomology. Galois group action allows to organize quantum states into multiplets of Galois groups acting as symmetry groups of physics. Poincare duality would map the analogs of fermionic creation operators to annihilation operators and vice versa and the counterpart of pairing of k:th and n-k:th homology groups would be inner product analogous to that given by Grassmann integration. The interpretation in terms of fermions turns however to be wrong and the more appropriate interpretation is in terms of Dolbeault cohomology applying to forms with homomorphic and antiholomorphic indices. - The intuitive idea that the Galois group is analogous to 1-D homotopy group which is the only non-commutative homotopy group, the structure of infinite primes analogous to the braids of braids of braids of ... structure, the fact that Galois group is a subgroup of permutation group, and the possibility to lift permutation group to a braid group suggests a representation as flows of 2-D plane with punctures giving a direct connection with topological quantum field theories for braids, knots and links. The natural assumption is that the flows are induced from transformations of the symplectic group acting on δ M
^{2}_{+/-}× CP_{2}representing quantum fluctuating degrees of freedom associated with WCW ("world of classical worlds"). Discretization of WCW and cutoff in the number of modes would be due to the finite measurement resolution. The outcome would be rather far reaching: finite measurement resolution would allow to construct WCW spinor fields explicitly using the machinery of number theory and algebraic geometry. - A connection with operads is highly suggestive. What is nice from TGD perspective is that the non-commutative generalization homology and homotopy has direct connection to the basic structure of quantum TGD almost topological quantum theory where braids are basic objects and also to hyper-finite factors of type II
_{1}. This notion of Galois group makes sense only for the algebraic varieties for which coefficient field is algebraic extension of some number field. Braid group approach however allows to generalize the approach to completely general polynomials since the braid group make sense also when the ends points for the braid are not algebraic points (roots of the polynomial).

This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions.

*2. p-Adic integration and cohomology*

This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.

- The calculation of twistorial amplitudes reduces to multi-dimensional residue calculus. Motivic integration gives excellent hopes for the p-adic existence of this calculus and braid representation would give space-time representation for the residue integrals in terms of the braid points representing poles of the integrand: this would conform with quantum classical correspondence. The power of 2π appearing in multiple residue integral is problematic unless it disappears from scattering amplitudes. Otherwise one must allow an extension of p-adic numbers to a ring containing powers of 2π.
- Weak form of electric-magnetic duality and the general solution ansatz for preferred extremals reduce the Kähler action defining the Kähler function for WCW to the integral of Chern-Simons 3-form. Hence the reduction to cohomology takes places at space-time level and since p-adic cohomology exists there are excellent hopes about the existence of p-adic variant of Kähler action. The existence of the exponent of Kähler gives additional powerful constraints on the value of the Kähler fuction in the intersection of real and p-adic worlds consisting of algebraic partonic 2-surfaces and allows to guess the general form of the Kähler action in p-adic context.
- One also should define p-adic integration for vacuum functional at the level of WCW. p-Adic thermodynamics serves as a guideline leading to the condition that in p-adic sector exponent of Kähler action is of form (m/n)
^{r}, where m/n is divisible by a positive power of p-adic prime p. This implies that one has sum over contributions coming as powers of p and the challenge is to calculate the integral for K= constant surfaces using the integration measure defined by an infinite power of Kähler form of WCW reducing the integral to cohomology which should make sense also p-adically. The p-adicization of the WCW integrals has been discussed already earlier using an approach based on harmonic analysis in symmetric spaces and these two approaches should be equivalent. One could also consider a more general quantization of Kähler action as sum K=K_{1}+K_{2}where K_{1}=rlog(m/n) and K_{2}=n, with n divisible by p since exp(n) exists in this case and one has exp(K)= (m/n)^{r}× exp(n). Also transcendental extensions of p-adic numbers involving n+p-2 powers of e^{1/n}can be considered. - If the Galois group algebras indeed define a representation for WCW spinor fields in finite measurement resolution, also WCW integration would reduce to summations over the Galois groups involved so that integrals would be well-defined in all number fields.

*3. Floer homology, Gromov-Witten invariants, and TGD*

Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups
by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M^{4}_{+/-}× CP_{2} define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings.

One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional.

The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry.

Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M^{4}× CP_{2} and in CP_{3}× CP_{3} with space-time surfaces replaced with 6-D sphere bundles.

*4. K-theory, branes, and TGD *

K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed.

*5. p-Adic space-time sheets as correlates for Boolean cognition*

p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2^{n}>p>p^{n-1} statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.

[68] **viXra:1111.0088 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 17 pages.

Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open.

The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously.

An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature.

[67] **viXra:1111.0087 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 4 pages.

The vanishing of ordinary determinant tells that a group of linear equations possesses non-trivial solutions. Hyperdeterminant generalizes this notion to a situation in which one has homogenous multilinear equations. The notion has applications to the description of quantum entanglement and has stimulated interest in physics blogs. Hyperdeterminant applies to hyper-matrices with n matrix indices defined for an n-fold tensor power of vector space - or more generally - for a tensor product of vector spaces with varying dimensions. Hyper determinant is an n-linear function of the arguments in the tensor factors with the property that all partial derivatives of the hyper determinant vanish at the point, which corresponds to a non-trivial solution of the equation. A simple example is potential function of n arguments linear in each argument.

Why the notion of hyperdeterminant- or rather its infinite-dimensional generalization- might be interesting in TGD framework relates to the quantum criticality of TGD stating that TGD Universe involves a fractal hierarchy of criticalities: phase transitions inside phase transitions inside... At classical level the lowest order criticality means that the extremal of Kähler action possesses non-trivial second variations for which the action is not affected. The system is critical. In QFT context one speaks about zero modes. The vanishing of the so called Gaussian (of functional) determinant associated with second variations is the condition for the existence of critical deformations. In QFT context this situation corresponds to the presence of zero modes.

The simplest physical model for a critical system is cusp catastrophe defined by a potential function V(x) which is fourth order polynomial. At the edges of cusp two extrema of potential function stable and unstable extrema co-incide and the rank of the matrix defined by the potential function vanishes. This means vanishing of its determinant. At the tip of the cusp the also the third derivative vanishes of potential function vanishes. This situation is however not describable in terms of hyperdeterminant since it is genuinely non-linear rather than only multilinear.

In a complete analogy, one can consider also the vanishing of n:th variations in TGD framework as higher order criticality so that the vanishing of hyperdeterminant might serve as a criterion for the higher order critical point and occurrence of phase transition. Why multilinearity might replace non-linearity in TGD framework could be due to the non-locality. Multilinearty with respect to imbedding space-coordinates at different space-time points would imply also the vanishing of the standard local divergences of quantum field theory known to be absent in TGD framework on basis of very general arguments. In this article an attempt to concretize this idea is made. The challenge is highly non-trivial since in finite measurement resolution one must work with infinite-dimensional system.

[66] **viXra:1111.0086 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 45 pages.

There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS_{5}× S^{5} background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved.

In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra.

Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP_{2}. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP_{2} allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP_{3}× CP_{3} mapped to 6-surfaces dual CP_{3}× CP_{3}, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action.

[65] **viXra:1111.0085 [pdf]**
*submitted on 1 Nov 2011*

**Authors:** Matti Pitkänen

**Comments:** 17 pages.

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II_{1} (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λ_{i}) for a positive integer valued variable n characterized by rational-valued parameters λ_{i} is obtained by replacing n and the integers characterizing λ_{i} with so called quantum integers depending on the quantum phase q_{m}=exp(i2π/m). Quantum integer n_{q} must be defined as the product of quantum counterparts p_{q} of the primes p appearing in the prime decomposition of n. One has p_{q}= sin(2π p/m)/sin(2π/m) for p≠ P and p_{q}=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers P^{n} to P^{-n} and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ P_{n})=∑ I(P_{n}). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n^{+}n^{-}, n^{+}_{q}>0 with fixed n^{-}_{q}<0,
are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ k_{p}Δ R/R and Δ m/m≈ k_{m}Δ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

[64] **viXra:1110.0030 [pdf]**
*submitted on 9 Oct 2011*

**Authors:** Dan Visser

**Comments:** 7 pages

A theoretical calculation with a new dark energy force formula discloses the correctness of the
experimental faster-than-light-neutrinos in the CERN-San Grasso experiment. The formulation in this paper
theoretically confirms that Einstein's Relativity could be violated. This introduces the obligation to accept
a new cosmological model, called the Double Torus hypothesis . The theoretical calculation in this paper
is based on a new momentum of dark energy force, formulated by its new force and two extra time dimensions
below the Planck scale. In detail this completely new perspective shows that the dark energy force starts
to dominate the lowest limit of the Newton-force-acceleration under specific conditions of
neutrino-oscillations. This paper theoretically calculates 62.8 nanosecond for the experimental detected
early-arrival of muon-neutrinos related to how light-in-vacuum would have arrived. This is a marvelous
close match compared to the ((60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanosecond found during the 'neutrino-flight
path' from CERN to San Grasso.

**Category:** Mathematical Physics

[63] **viXra:1109.0038 [pdf]**
*submitted on 18 Sep 2011*

**Authors:** Markos Georgallides

**Comments:** 9 pages

This article explains the correlation between Euclidean Geometry , Complex Numbers and Physics .
A Straight line AB is continuous in Points between A and B [ i.e. all points between AB are the elements which fill AB ] , which Points are also , Nothing , Everything , and maybe Anywhere , without any Dimension , and one has to
pass the infinite points between A and B . A point C is on line AB only when exists CA+ CB = AB , or the whole AB is equal to the parts CA , CB , and this
is an equation , which differentiates geometries .
Since points have not any dimension and since only AB has dimension ( the length AB and for ÃC the length AC ) and since on ÃB exist infinite AC → AB , which
have infinite Spaces , Anti-Spaces and Sub-Spaces , then
1. Straight line AB is continuous with points as filling ( Infinitively divisible ) .
2. Straight line AB is discontinuous (discrete) with dimensional Units , ds =AB
as filling ( that is made up of finite divisible or indivisible parts the Monads ds )
or ds → AB / n , where n = 1 , 2 , → ∞ ) , and for n = ∞ then ds = 0 .
3. Straight line AB is discontinuous (discrete) with dimensional Units ds , or
ds = quantum = AB / n [ where n = 1,2,3 → ∞ , = ( a + b.i ) / n , Infinitively
divisible and keeping always the conservation of properties at end points A , B ]
as filling , and continuous with points as filling ( for n = ∞ then ds = 0 i.e.
a point ) . This is the Vector relation of Monads , ds , ( or , as Complex
Numbers in their general form , ds = a + b. i ) , which is the Dual
Nature of lines AB , ( discrete and continuous ) . So travelling on Points
( ds = 0 ) between AB one never comes to B , on the contrary travelling
with ds > 0 one comes in finite time .
4 . Achilles has to pass every point of line AB which is then as passing from
the starting point A , ds =0 , where Velocity of Achilles is v(A) = ds/dt = 0 .
The same happens for Tortoise at point B where Velocity v(T) = ds/dt = 0 .
On the contrary , Achilles passing AB on dimensional Units , ds , then Achilles velocity v(A) = ds/dt(A) is greater than that of Tortoise v(T) = ds / dt(T) .
Since in PNS , v = ∞ , T = 0 , meaning infinite velocity and Time not existing , then
Arrow AB in [PNS] is constant because AB = ds = Constant = u . 0 = ∞ . 0 Straight line AB is discontinuous (discrete) with dimensional Units ds = AB / n
where n = 1 → ∞ and continuous with points [ n = ∞ ] . Continuously on AB happens also with all discrete ds , ( This is the Dual Nature of lines ( Geometry ), discrete and continuous ) .
Monads ds = 0 → ∞ are Simultaneously , actual infinite ( because for n = ∞ then ds = [ AB / n = ∞ ] = 0 i.e. a point ) , and potential infinite , ( because for
n = 0 then ds = [ AB / n=0 ] = ∞ i.e. the straight line through AB .

**Category:** Mathematical Physics

[62] **viXra:1109.0034 [pdf]**
*submitted on 16 Sep 2011*

**Authors:** Giuliano Bettini

**Comments:** 24 pages.

There is a lot of chattering on the Internet about Tesla waves, vacuum energy, scalar waves and so
on. Professor Meyl says he has a complete theory, experimental evidence and apparatus on these
waves. In a theoretical paper Van Vlaenderen introduced a generalization of classical
electrodynamics for the prediction of scalar field effects. It is said the Monstein has demonstrated
the physical existence of such scalar waves. NASA in a report seems to consider such waves as a
promising item to be studied. Some other papers appeared in arXiv.
I've already showed that such waves are a consequence of "generalized" Maxwell fields which
simply mean space time analytic functions not limited by the Lorenz gauge condition, but accepted
instead in a wide sense.
In this paper I remember my ideas on these waves, together with my doubts about their physical
existence. In fact, the deduction of the scalar waves equations, together with their physical
interpretation, in my opinion demonstrates nothing about the physical existence of scalar waves.
I discuss the experiment of Monstein, and suggest some other experiment.
Obviously I think that the lack of demonstration of the existence doesn't mean the demonstration of
inexistence.

**Category:** Mathematical Physics

[61] **viXra:1108.0048 [pdf]**
*submitted on 29 Aug 2011*

**Authors:** Dan Visser

**Comments:** 4 pages. Publication is free for any institute or magazine

The Higgs mass is approximately 0.5 TeV/c2 . This is a new predicted value. This
mass value for Higgs is calculated with a new dark energy force formula, which is performing in
the hypothesis of the Double Torus, a new cosmological "model" for the universe. This "model"
embeds the Big Bang framework. The new Higgs mass is theoretically disclosed by implementing the
dimensional features of relativistic spacetime into the dimensions of the dark energy force formula and an
equalization to the lowest limit for acceleration in Newton force, being a transition where Newton breaks down
and the dark energy force takes over. The dark energy force generates gravitational movement and thus mass. This
enables to calculate a Higgs mass differently than in currently used theories.

**Category:** Mathematical Physics

[60] **viXra:1108.0047 [pdf]**
*submitted on 27 Aug 2011*

**Authors:** Giuliano Bettini

**Comments:** 21 pages.

I present examples of applications of 3-dimensional analytic functions to electrostatics and potential
flows, mainly devoted to engineers and physicists.
Of course, the paper only suggests areas of future development, despite that a persistent idea, from
Sommerfeld on, seems to be "The powerful tool of the theory of complex functions cannot be used
in three-dimensional potential theory" (Sommerfeld, "Mechanics of Deformable Bodies",
Academic Press, 1950)
I summarize here unpublished manuscripts dated 1994.

**Category:** Mathematical Physics

[59] **viXra:1108.0042 [pdf]**
*submitted on 26 Aug 2011*

**Authors:** Valeriy V. Dvoeglazov

**Comments:** 19 Pages

We introduce the Majorana spinors in the momentum representation.
They obey the Dirac-like equation with eight components, which has been
first introduced by Markov. Thus, the Fock space for corresponding quantum
fields is doubled (as shown by Ziino). Particular attention has been
paid to the questions of chirality and helicity (two concepts which frequently
are confused in the literature) for Dirac and Majorana states.

**Category:** Mathematical Physics

[58] **viXra:1108.0005 [pdf]**
*submitted on 2 Aug 2011*

**Authors:** D.T. Froedge

**Comments:** 14 pages

In a previous paper we have discussed the conjecture of a variable particle rest mass, as a
function of gravitational potential (Scalar Gravitational Theory with Variable Rest Mass)
This paper discuses the implications of that theory in regard to a large neutron star, and
contrast the difference between the predicted phenomena, and Black Hole theory as put fourth by
standard GR. The validity of this theory would be established by the finding of a neutron star having a
mass greater than allowed by Black Hole theory.

**Category:** Mathematical Physics

[57] **viXra:1107.0062 [pdf]**
*submitted on 31 Jul 2011*

**Authors:** D.T. Froedge

**Comments:** 16 pages

The purpose of this paper is to present a non-tensor theory of gravitation that
provides the equivalent equations of motion, but does not result in the issue
of black holes, non-localizable energy, or spacetime singularities. The prime
assumption is the notion that the rest mass of a particle entering a
gravitational potential is reduced in proportion to the energy gained by the
velocity increases. One could designate this development as a "catalytic"
theory in that gravitation is a vector catalyst, that converts rest energy into
kinetic energy. The total mass energy will be considered localized with the
individual mass particles, and defined relative to a given observer. No
energy will be ascribed to the field, thus there is no stress energy tensor. We
will develop the energy mass relation, and show that it can result in the
proper orbital precession as demonstrated by GR. The rest mass is not
significantly different from that of a particle defined in a stationary
asymptotically flat GR space-time, when the defining point particles via the
Komar mass. Since rest mass of a particle goes to zero on approaching a
Schwarzschild boundary, the formation of black holes becomes problematic.

**Category:** Mathematical Physics

[56] **viXra:1107.0042 [pdf]**
*submitted on 21 Jul 2011*

**Authors:** Dan Visser

**Comments:** 4 pages

September 1 2009 a new cosmological hypothesis was proposed to imagine the
universe otherwise. Many institutional scientists still try to implement their results into the
commonly accepted Big Bang theory. I am one of the two scientists who propose a
Double Torus as a new shape for the universe. Several 'papers' are hosted at 'vixra' about
this subject. This paper adds an explanaition to these afore published papers and in
particular explains the 'dominance of matter over anti-matter', deduced from the earlier
derived 'dark energy force formula' and the perspective of the Double Torus.

**Category:** Mathematical Physics

[55] **viXra:1107.0017 [pdf]**
*submitted on 10 Jul 2011*

**Authors:** Dan Visser

**Comments:** 5 pages

Here in this 'paper' a deeper analysis of the 'dark energy force formula' in the
Double Torus Cosmology is made. Earlier 'papers' were posted as 'pre-papers' in the
vixra-archive. These are subject to a new cosmological hypothesis, being further described
in higher order mathematics in the near future by Christopher Forbes. I have found
evidence through an unexpected interpretation of CMB results, that the 'dark energy force
formula' appears to be a functional 'recalculation-mechanism' for quantum gravity.

**Category:** Mathematical Physics

[54] **viXra:1106.0059 [pdf]**
*submitted on 27 Jun 2011*

**Authors:** Sangwha Yi

**Comments:** 6 pages.

In the special relativity theory, study the gauge theory in the Electro-magnetic field theory.Using that the
Electro-magnetic potential is 4-vector, treat invariant potential. And the Electro-Magnetic field theory's
the gauge theory expand.

**Category:** Mathematical Physics

[53] **viXra:1106.0018 [pdf]**
*submitted on 11 Jun 2011*

**Authors:** Sergey V. Ershkov

**Comments:** 6 pages

Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.

**Category:** Mathematical Physics

[52] **viXra:1105.0033 [pdf]**
*submitted on 23 May 2011*

**Authors:** Dan Visser

**Comments:** 5 pages

Three new cosmological models are 'circling' the science-community: a 'Bouncing
Universe', a 'Conformal Cyclic Cosmology and a 'Double Torus Cosmology'. All new
ideas, commented anonymously and discussed institutionally. This paper wants more
cosmologists and physicists to involve the discussion openly in the media, without walking
save roads. The authors and readers are invited to involve this discussion. Which model is
true and can the mathematics be matched?

**Category:** Mathematical Physics

[51] **viXra:1105.0022 [pdf]**
*submitted on 15 May 2011*

**Authors:** Dan Visser

**Comments:** 6 pages

This paper shows how a 'dark energy force formula' emerges five more space- and
two more time-dimensions in nature. The 'formula' is earlier described in vixra-papers,
announcing the universe is a double torus of dark energy and dark matter. The 'formula' is
a completely different force than the cosmological constant of Einstein used to explain
accelerated expansion in the big bang. With this in mind, two independent experimental
investigations has given additional proof, that the 'dark energy force formula' correlates
the independent investigations, because: 1) Five extra space-dimensions have to exist,
according to how electrons behave in graphene-experiments. 2) Computer-simulation
shows a double torus geometry, that emerges from two colliding blackholes involving a
third torus during pulsation. These results match with the postulate that the universe exists
of a double torus of dark energy and dark matter, including a 'dark energy force formula'.

**Category:** Mathematical Physics

[50] **viXra:1105.0016 [pdf]**
*submitted on 12 May 2011*

**Authors:** Subhajit Ganguly

**Comments:** 10 pages.

Considering transport of light through space-time, following the laws of physical transactions
(viXra:1101.0035) it may be said that there must be a spreading effect on it. Over suitable distances from
a source of light, an observer's perception is bound to be affected due to this spreading. In the following
paper, these effects on the reception of a signal, due to the spreading of light are studied. Experimental
set-ups are desired to verify the actual angles of spread with their theoretical values. An experiment
regarding the minimum distance between two disturbances for them to be distinguishable is also carried
out. The energy quantum is also studied in a new light.

**Category:** Mathematical Physics

[49] **viXra:1104.0085 [pdf]**
*submitted on 28 Apr 2011*

**Authors:** Dan Visser

**Comments:** 8 pages

For the first time an announcement is made in this paper to have found
fundamental evidence for the flyby-anomalies of six satelites earlier investigated by John
Anderson and coworkers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The
central part of this theoretical evidence exists of a 'dark matter impuls flow' being the
cause of a velocity-change for satelites during their 'flyby' along the earth. A formula is
given to calculate the velocity-change caused by dark matter. Also a dark matter constant
is suggested. The origin of the evidence is related to a 'dark energy force formula', which
is a new force in a new proposed cosmological model describing dark energy and dark
matter in a double torus geometry (TTM). Originally the 'dark energy force formula' is
discovered by an independent cosmologist and E-ingenieur, Dan Visser from Almere, the
Netherlands. Then afterwards a few 'papers' have been published in the vixra-archive
since September 1 2009 in colaboration with mathematician and physicist Christopher
Forbes (UK). These 'papers' could be considered as 'pre-exercises' in awaiting for a more
robust mathematical framework for the new proposed double torus cosmological model.

**Category:** Mathematical Physics

[48] **viXra:1103.0115 [pdf]**
*submitted on 30 Mar 2011*

**Authors:** José Francisco García Juliá

**Comments:** 3 pages

We consider that the action at a distance is carried out by virtual carriers of the force,
which are created and annihilated in the vacuum by the field in a time less than that of
the Heisenberg's uncertainty.

**Category:** Mathematical Physics

[47] **viXra:1103.0114 [pdf]**
*submitted on 30 Mar 2011*

**Authors:** Jalil Olia, Vahid Afshinmehr

**Comments:** 20 pages

In this paper we applied a finite element method to finding the effects on the
reverberation times of common irregularities like curved surfaces, non-parallel walls
and large open-walled ante-rooms, found in auditoria. The number of modes having
a reverberation time in a specified time interval is expressed as a function of the
total allowed degrees of freedom and it is shown that even when the number of
degrees of freedom of the model is large there is, in general, no one dominant group.
Curved surfaces in particular lead to a situation where some modes have very long
reverberation times, leading to bad acoustics. In such situations a knowledge of the
offending mode shapes give an indication on where to position absorptive material
for optimum effect.

**Category:** Mathematical Physics

[46] **viXra:1103.0012 [pdf]**
*submitted on 3 Mar 2011*

**Authors:** Dan Visser, Chris Forbes

**Comments:**
7 pages.

Particularly this paper announces dark energy could be measured as a
cosmic backround (CMB)-frame related to a specific quantumstate of dark
energy and dark matter conform a double torus cosmology (TTM[1,2,3,4,5,6,7]).
In addition this paper also refers to a planned dark energy interferometerproject
expected to be operational in 2014[8]. Both aspects can be combined
in order to get a better expectation and interpretation of the detection of dark
energy. This paper shows dark energy to interact differently than in the
planned experiments of the dark energy interferometer-project. That is the
motive to publish this paper. Benchmark is dark energy and dark matter are
not considered in a big bang cosmology, but in a double torus universe of one
torus of dark energy, which encloses and intertwines a second torus of dark
matter (TTM-cosmology). In derivations is shown that dark energy will affect
falling (super positioned) Cesium atoms in the dark energy interferometerproject
unexpectedly: 1. It will touch the super-positioned atoms twice! ; the
cause will be the torus-geometry of the TTM-derived CMB-frame. 2. The
'Twice-touching' will vary subsequently; the cause will be a dependency on
'expansion or contraction' of the CMB-torus geometry through dynamics that
are caused by the "+" and "-" strength of the dark energy force in the TTM
and which is produced by the dark energy torus. This has motivated me to
calculate a specific value for TTM-dark energy on about 4 x 10^{-114} [X.s] in
6.4 x 10^{-48} [m^{2}] as a new sort of spin-quantumstate [X.s], which drives the
expansion of big bang cosmology analogue to how elementary spin is a
'generator for rotation' in conventional quantumphysics. Probably this paper
might be of interest to the dark energy interferometer-project at least.

**Category:** Mathematical Physics

[45] **viXra:1102.0037 [pdf]**
*submitted on 21 Feb 2011*

**Authors:** Ayind T Mahamba

**Comments:**
8 Pages. Submissions for FQXi essay contest.

The quest to explain the true nature of reality is one of the great scientific goals. In fact, this essay contest
asks: is Nature fundamentally continuous or discrete and how can these two different but very useful concepts be
fully reconciled? Physical science is vast, complex and remains mysterious [10]. Since long ago, the great thinkers
and scholars have dedicated their lives to the attempted comprehension1 of this reality that has become so abstract.
Throughout the centuries and through experimentation, they have established numerous laws, concepts, theories,
and principles concerning the fundamental notions of reality (centered on matter-energy and spacetime). I propose a
central theory (MIT), based on the information of, and compatible with, the contemporary scientific knowledge; the
existing fundamental relation between the "physical entities" passes through the determined quantitative
transmission (quantity) of this preserved transcendent greatness (quality). In addition to a "formal" relationship
(existence) which creates an informal description of what is real, there is a causal relationship between
"phenomena" (relativity). My informational approach has been productive in several domains where many enigma
persist; solutions for these problems must be envisaged globally, using ideas and concepts from numerous different
fields, with a coherent schema...
The "Theory of Universal Relativity" (TUR as a ToE) proposed here lays bridges between domains which, at first
glance, have nothing to do with each other; it also provides insight into how we can improve our knowledge by
understanding the interplay of complexity and simplicity. Therefore emerging from simplexity (contraction of
simplicity and complexity), reality is both digital and analogue (and between) and also more! We know there is a
strange and mysterious world that surrounds us, a world largely hidden from our senses with extra dimensions and
as a mathematical concept of reality, MIT may confirm that we are part of a cosmic hologram (a paradigm shift).
My theory has the advantage of being extremely simple, not limited to scientists because everyone can understand it
(I = 1 ± i). So, in this essay, I will try to explain why and how [1][13][48][51].

**Category:** Mathematical Physics

[44] **viXra:1102.0032 [pdf]**
*submitted on 19 Feb 2011*

**Authors:** Malcolm Macleod

**Comments:**
3 pages.

This paper suggests a 'quantity of momentum', a square root of Planck momentum,
here referred to as Quintessence-momentum, as a natural unit that is common to both
mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine
structure constant) and c; geometrical formulas for the natural physical constants and
the electron mass are proposed. Results are consistent with CODATA 2006.

**Category:** Mathematical Physics

[43] **viXra:1102.0027 [pdf]**
*submitted on 17 Feb 2011*

**Authors:** Sergey G. Fedosin

**Comments:**
5 pages. In Russian

The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the
perspective of the physical implementation of well-studied four-and n-dimensional geometric objects.
Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime.

**Category:** Mathematical Physics

[42] **viXra:1102.0009 [pdf]**
*submitted on 7 Feb 2011*

**Authors:** Daniele Sasso

**Comments:** 7 pages, 5 figures.

The criteria of stability defined in the standard theory of linear systems aren't
exhaustive and show some inconsistencies. In this article we define new
criteria of stability more consistent with real physical situations. In particular
we distinguish between static stability and dynamic stability in order to analyse
the stability of systems in the time domain and in Laplace's equivalent
domain. Let introduce then the frequency stability in order to analyse the
stability of systems in the Fourier domain.

**Category:** Mathematical Physics

[41] **viXra:1101.0096 [pdf]**
*submitted on 29 Jan 2011*

**Authors:** Dan Visser, Christopher Forbes

**Comments:** 10 pages

This paper postulates a theoretical structure within entangled photons.
The postulate is introduced within the framework of the cosmological
Twin-Tori Model (TTM). Related papers are to be found in viXra[1,2,3,4,5,6]. After
generally derived equations and interpretations, a mass (m_{t}) per 2π is
calculated on ~ 2.6 x 10^{-34} [(J.s) m^{2} / s]. Such a tiny spinning-forward surface
per second (torus geometry) has an energy much smaller than the Planckenergy
in Joule, suggesting a subdivision of 10^{43} surfaces below the
Planckscale: If one photon changes spin, the entangled photon could follow
by means of the spinning-forward tiny surface-structure within the torus
geometry (per 2π), being an information-flux for entanglement in general
below the Planckscale.

**Category:** Mathematical Physics

[40] **viXra:1101.0052 [pdf]**
*submitted on 16 Jan 2011*

**Authors:** Giuliano Bettini

**Comments:** 10 pages

In a preceding paper we introduced a conjecture: the classification of the 32 crystal classes with 5
bits. In the present paper we will review our preceding result, and continue showing some further
interesting issues. In the paper, it is argued that bits should be identified with five basic unknown
symmetries generating these 32 groups. Probably it is not merely a coincidence that 32 means 5
bits. And probably is it not merely a coincidence that each complete subset of bits (properties)
means the holohedry of a crystal system; and each new bit means a new crystal system.
The purpose of this article was of course not to draw a conclusive theory, but to suggest ideas that,
we hope, will be useful for researchers in mathematics, group theory and crystallography.

**Category:** Mathematical Physics

[39] **viXra:1101.0037 [pdf]**
*submitted on 11 Jan 2011*

**Authors:** Ke Xiao

**Comments:** 5 pages

The fine structure constant α = e^{2}/hc ~ 1/137.036 and the blackbody
radiation constant α_{R} = e^{2}(a_{R}/k^{4}_{B})^{1/3} ~ 1/157.555
are linked by prime numbers. The blackbody radiation constant is a new method to measure
the fine structure constant. It also links the fine structure constant to the
Boltzmann constant.

**Category:** Mathematical Physics

[38] **viXra:1101.0035 [pdf]**
*submitted on 10 Jan 2011*

**Authors:** Subhajit Ganguly

**Comments:** 15 pages

Considering transport or tendency ... (see paper)

**Category:** Mathematical Physics

[37] **viXra:1012.0052 [pdf]**
*submitted on 29 Dec 2010*

**Authors:** Giuliano Bettini

**Comments:** 9 pages, in Italian

There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.

**Category:** Mathematical Physics

[36] **viXra:1012.0031 [pdf]**
*submitted on 14 Dec 2010*

**Authors:** Elemér E Rosinger

**Comments:** 9 pages

A class of non-Cartesian physical systems, [7], are those whose
composite state spaces are given by significantly extended tensor products.
A more detailed presentation of the way such extended tensor products
are constructed is offered, based on a step by step comparison with the
construction of usual tensor products. This presentation clarifies the
extent to which the extended tensor products are indeed more general
than the usual ones.

**Category:** Mathematical Physics

[35] **viXra:1012.0020 [pdf]**
*submitted on 8 Dec 2010*

**Authors:** Elemer E Rosinger

**Comments:** 6 pages

The following open problem is presented and motivated : Are there
physical systems whose state spaces do not compose according to either
the Cartesian product, as classical systems do, or the usual tensor
product, as quantum systems do ?

**Category:** Mathematical Physics

[34] **viXra:1012.0014 [pdf]**
*submitted on 4 Dec 2010*

**Authors:** Elemer E Rosinger

**Comments:** 28 pages

Much of Mathematics, and therefore Physics as well, have been
limited by four rather consequential restrictions. Two of them are ancient
taboos, one is an ancient and no longer felt as such bondage, and the
fourth is a surprising omission in Algebra. The paper brings to the
attention of those interested these four restrictions, as well as the fact
that each of them has by now ways, even if hardly yet known ones, to
overcome them.

**Category:** Mathematical Physics

[33] **viXra:1012.0002 [pdf]**
*submitted on 1 Dec 2010*

**Authors:** Arkadiusz Jadczyk

**Comments:** 7 pages, To appear in Advances in Applied Clifford Algebras

We study in some detail the structure of the projective quadric Q'
obtained by taking the quotient of the isotropic cone in a standard pseudohermitian
space H_{p,q} with respect to the positive real numbers R^{+} and,
further, by taking the quotient ~Q = Q'/U(1). The case of signature (1. 1)
serves as an illustration. ~Q is studied as a compactification of RxH_{p-1,q-1}

**Category:** Mathematical Physics

[32] **viXra:1011.0039 [pdf]**
*submitted on 17 Nov 2010*

**Authors:** Guy Moore, Richard Moore

**Comments:** 40 pages

Our obtaining the analytical equations for the gravitation of a particular type of
mathematical annulus, which we called a 'Special Gravitating Annulus' (SGA), greatly
facilitates studying its orbital properties by computer programming. This includes
isomorphism, periodic and chaotic polar orbits, and orbits in three dimensions.
We provide further insights into the gravitational properties of this annulus and
describe our computer algorithms and programs. We study a number of periodic orbits,
giving them names to aid identification.
'Ellipses extraordinaires' which are bisected by the annulus, have no gravitating
matter at either focus and represent a fundamental departure from the normal association
of elliptical orbits with Keplerian motion. We describe how we came across this type of
orbit and the analysis we performed. We present the simultaneous differential equations
of motion of 'ellipses extraordinaires' and other orbits as a mathematical challenge. The
'St.Louis Gateway Arch' orbit contains two 'instantaneous static points' (ISP).
Polar elliptical orbits can wander considerably without tending to form other kinds
of orbit. If this type of orbit is favoured then this gives a similarity to spiral galaxies
containing polar orbiting material.
Annular oscillatory orbits and rotating polar elliptical orbits are computed in
isometric projection. A 'daisy' orbit is computed in stereo-isometric projection.
The singularity at the centre of the SGA is discussed in relation to mechanics and
computing, and it appears mathematically different from a black hole.
In the Appendix, we prove by a mathematical method that a thin plane self-gravitating
Newtonian annulus, free from external influence, exhibiting radial gravitation that varies
inversely with the radius in the annular plane, must have an area mass density which
also varies inversely with the radius and this exact solution is the only exact solution.

**Category:** Mathematical Physics

[31] **viXra:1010.0063 [pdf]**
*submitted on 29 Oct 2010*

**Authors:** Dan Visser

**Comments:** 7 pages

A new surface energy-value for dark matter is calculated, derivated from a
perspective of a "higher order universe". A universe of dark energy, dark- and visible
matter, and a dark energy force. A fundamental connection between dark matter and
visible matter is related to dark energy (viXra-paper 1010.0014 in particular is the
reference for this novum [5]. The surface energy-density of dark matter seems to be a
factor 5 to 20 times higher than earlier predicted value-ranges by the CDMS-project and
the Fermi-satelite. Also the produced energies through particle-collissions by LHC CERN
will not be enough to achieve the dark matter surface energy-value. The "fact" some of
these projects have announced some vaque "bliebs" might be due to a new phenomenon in
the search of dark matter. It could be caused by "three dimensional time", which is
embedded as a "new duality" in the new model, the "Twin-Tori cosmological Model
(TTM)"[1,2,3,4]. The "three dimensional time" might cause dark matter taking unknown
paths before detection. This paper has calculated the surface energy-density value for
dark matter on 1 TeV in a surface of 6.4 x 10 ^{-48} [m2].

**Category:** Mathematical Physics

[30] **viXra:1010.0036 [pdf]**
*submitted on 24 Oct 2010*

**Authors:** Debayan Dasgupta

**Comments:** 10 pages

The main purpose of this paper is to show the application of mathematical system
of quaternions in physics. We show a basic way of generating a quaternion
operator and a method of obtaining the Schrodinger's equation using this
operator matrix. Then we investigate the various probable uses of the coefficient
matrix to scale relativity and spacetime quantization.

**Category:** Mathematical Physics

[29] **viXra:1010.0014 [pdf]**
*submitted on 7 Oct 2010*

**Authors:** Dan Visser

**Comments:** 5 pages

A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a
dark energy force F_{de} , which empowers the dynamic of a lower order universe, well
known as the big bang. In this paper I introduce the 1st derivative F'_{de} of this dark energy
force to reveal deeper properties of the TTM, such as: why quantummechanics exists in
the big bang, why dark matter and visible matter are equally responsible for gravity in
galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe
is recalculated by subquantumlevel-information below the Plancklength, and why the
impression of space-expansion is due to the higher order cosmological model TTM.

**Category:** Mathematical Physics

[28] **viXra:1009.0007 [pdf]**
*submitted on 3 Sep 2010*

**Authors:** D.T. Froedge

**Comments:**
16 pages 38 equations 98kb

The purpose of this paper is to illustrate a fundamental, multiple particle,
system equation for which the Klein-Gordon-Dirac-Schrödinger equations are
single particle special cases. In the same manner that eigenvalues of the
Schrödinger equation represents energy levels of an interacting atomic system,
eigenvalues represent particle energies in an interacting system of particles. An
equation is proposed that has vector solutions defined in Dirac, or Clifford
algebra, that treats a collection of particles as a single system..The proposed
solution is a descriptor of a symmetric, light speed expanding group of
interacting particles having real, as well as the familiar QM constituents.

**Category:** Mathematical Physics

[27] **viXra:1007.0031 [pdf]**
*submitted on 19 Jul 2010*

**Authors:** T. E. Raptis

**Comments:** 13 pages.

We report on a new general class of solutions of the Beltrami equation, with
special characteristics. We also provide examples of solutions that also satisfy Maxwell equations.
A subset of these solutions can be isolated which corresponds to "gauge" fields. A special
projective geometry of vacuum fields is also revealed and discussed.

**Category:** Mathematical Physics

[26] **viXra:1006.0070 [pdf]**
*submitted on 30 Jun 2010*

**Authors:** Carey R Carlson

**Comments:** 16 pages.

Quantum theory is reconstructed using standalone causal sets. The frequency ratios
inherent in causal sets are used to define energy-ratios, implicating the causal link as the
quantum of action. Space-time and its particle-like sequences are then constructed from
causal links. A 4-D time-lattice structure is defined and then used to model neutrinos and
electron clouds, which together constitute a 4-D manifold. A 6-D time-lattice is used to
model the nucleons. The integration of the nucleus with its electron cloud affords
calculation of the mass-ratio of the proton (or the neutron) with respect to the electron.
Arrow diagrams, along with several ball-and-stick models, are used to streamline the
presentation.

**Category:** Mathematical Physics

[25] **viXra:1006.0052 [pdf]**
*submitted on 21 Jun 2010*

**Authors:** Fredy Zypman

**Comments:**
2 pages

Formulas connecting toroidal functions and elliptical functions are useful in
various areas of physics. In solving a problem in electrostatics we run across
an error in the Handbook of mathematical functions of Abramowitz and
Stegun. In this paper we report the details.

**Category:** Mathematical Physics

[24] **viXra:1006.0042 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 13 Pages.

This appendix contains basic facts about CP_{2} as a symmetric space and Kähler manifold. The
coding of the standard model symmetries to the geometry of CP_{2}, the physical interpretation of
the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about
induced gauge fields are discussed

**Category:** Mathematical Physics

[23] **viXra:1006.0041 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 5 Pages.

The original justification for the hierarchy of Planck constants came from the indications that
Planck constant could have large values in both astrophysical systems involving dark matter and
also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also
factor spaces of CD and CP_{2} emerged from consistency conditions. It however seems that TGD
actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations
defined by Kähler action means that the correspondence between canonical momentum densities
and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the
introduction of the covering space of CD x CP_{2}, where CD denotes causal diamond defined as
intersection of future and past directed light-cones.

**Category:** Mathematical Physics

[22] **viXra:1006.0040 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 13 Pages.

The notion of electric magnetic duality emerged already two decades ago in the attempts to
formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable
step of progress took place in the understanding of this notion. This concept leads to the
identification of the physical particles as string like objects defined by magnetic charged wormhole
throats connected by magnetic
ux tubes. The second end of the string contains particle having
electroweak isospin neutralizing that of elementary fermion and the size scale of the string is
electro-weak scale would be in question. Hence the screening of electro-weak force takes place
via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic
duality leads also to a detailed understanding of how TGD reduces to almost topological quantum
field theory. A surprising outcome is the necessity to replace CP_{2} Kähler form in Kähler action
with its sum with S^{2} Kähler form.

**Category:** Mathematical Physics

[21] **viXra:1006.0039 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 16 Pages.

Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.

- One should perform the functional integral over WCW degrees of freedom for fixed values of on mass shell momenta appearing in the internal lines. After this one must perform integral or summation over loop momenta.
- One must define the functional integral also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.

[20] **viXra:1006.0038 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 37 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields, and infinite primes discussed in this
article.
The construction of infinite primes is formally analogous to a repeated second quantization of
an arithmetic quantum field theory by taking the many particle states of previous level elementary
particles at the new level. Besides free many particle states also the analogs of bound states
appear. In the representation in terms of polynomials the free states correspond to products of
first order polynomials with rational zeros. Bound states correspond to nth order polynomials
with non-rational but algebraic zeros.
The construction can be generalized to classical number fields and their complexifications
obtained by adding a commuting imaginary unit. Special class corresponds to hyper-octonionic
primes for which the imaginary part of ordinary octonion is multiplied by the commuting
imaginary unit so that one obtains a sub-space M^{8} with Minkowski signature of metric. Also in this
case the basic construction reduces to that for rational or complex rational primes and more
complex primes are obtained by acting using elements of the octonionic automorphism group which
preserve the complex octonionic integer property.
Can one map infinite primes/integers/rationals to quantum states? Do they have space-time
surfaces as correlates? Quantum classical correspondence realized in terms of modified Dirac
operator implies that if infinite rationals can be mapped to quantum states then the mapping of
quantum states to space-time surfaces automatically gives the map to space-time surfaces. The
question is therefore whether the mapping to quantum states defined by WCW spinor fields is
possible. A natural hypothesis is that number theoretic fermions can be mapped to real fermions
and number theoretic bosons to WCW ("world of classical worlds") Hamiltonians. The crucial
observation is that one can construct infinite hierarchy of hyper-octonionic units by forming
ratios of infinite integers such that their ratio equals to one in real sense: the integers have
interpretation as positive and negative energy parts of zero energy states. One can construct also
sums of these units with complex coefficients using commuting imaginary unit and these sums
can be normalized to unity and have interpretation as states in Hilbert space. These units can
be assumed to possess well defined standard model quantum numbers. It is possible to map the
quantum number combinations of WCW spinor fields to these states. Hence the points of M^{8}
can be said to have infinitely complex number theoretic anatomy so that quantum states of the
universe can be mapped to this anatomy. One could talk about algebraic holography or number
theoretic Brahman=Atman identity.
One can also ask how infinite primes relate to the p-adicization program and to the hierarchy of
Planck constants. The key observation is that infinite primes are in one-one correspondence with
rational numbers at the lower level of hierarchy. At the first level of hierarchy the p-adic norm
with respect to p-adic prime for this rational gives power p^{-n} so that one has two powers of p - p^{n+}
and p^{n-} since two infinite primes corresponding to fermionic vacua X±1, where X is the product
of all primes at given level of hierarchy, characterize the partonic 2-surface. The proposal inspired
by the p-adicization program is that Δφ = 2π/p^{n} defines angle measurement resolution crucial in
the construction of p-adic variants of WCW ("world of classical world") as a union of symmetric
coset spaces by starting from discrete variants of the real counterpart of symmetric space having
common points with tis p-adic variant. The two measurement resolutions correspond to CD and
CP_{2} degrees of freedom. The hierarchy of Planck constants generalizes imbedding space to a
book like structure with pages identified in terms of singular coverings and factor spaces of CD
and CP_{2}. There are good arguments suggesting that only coverings characterized by integers n_{a}
and n_{b}are realized. The identifications n_{+} and n

**Category:** Mathematical Physics

[19] **viXra:1006.0037 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 28 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields discussed in this article, and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory.
In this article the connection between standard model symmetries and classical number fields
is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of
classical worlds") is unique from its mere existence. This leads to its identification as union of
symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This
fixes space-time dimension and the decomposition M^{4} x S and the idea is that the symmetries
of the Kähler manifold S make it somehow unique. The motivating observations are that the
dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces,
and imbedding space and M^{8} can be identified as hyper-octonions- a sub-space of complexified
octonions obtained by adding a commuting imaginary unit. This stimulates some questions.
Could one understand S = CP_{2} number theoretically in the sense that M^{8} and H = M^{4} x CP_{2}
be in some deep sense equivalent ("number theoretical compactification" or M^{8} - H duality)?
Could associativity define the fundamental dynamical principle so that space-time surfaces could
be regarded as associative or co-associative (defined properly) sub-manifolds of M^{8} or equivalently
of H.
One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation
of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span
an associate (co-associative) sub-space at each point of space-time surface. Also M^{8} - H duality
holds true if one assumes that this associative sub-space at each point contains preferred plane of
M^{8} identifiable as a preferred commutative or co-commutative plane (this condition generalizes
to an integral distribution of commutative planes in M^{8}). These planes are parametrized by CP_{2}
and this leads to M^{8} - H duality.
WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford
algebra of M^{8} or H which are associative or co-associative. An open conjecture is that this
characterization of the space-time surfaces is equivalent with the preferred extremal property of
Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional
algebra of vanishing second variations.

**Category:** Mathematical Physics

[18] **viXra:1006.0036 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 51 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields (in particular, identifying associativity
condition as the basic dynamical principle), and infinite primes whose construction is formally
analogous to a repeated second quantization of an arithmetic quantum field theory. In this article
p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics
to a larger structure are discussed.
The basic technical problems relate to the notion of definite integral both at space-time level,
imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility
of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric
spaces can be used to define various integrals as sums over Fourier components. This leads to the
proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a
common intersection of these spaces, which basically reduces to an algebraic variant of coset space
involving algebraic extension of rationals by roots of unity. This brings in the notion of angle
measurement resolution coming as Δφ = 2π/p^{n} for given p-adic prime p. Also a proposal how
one can complete the discrete version of symmetric space to a continuous p-adic versions emerges
and means that each point is effectively replaced with the p-adic variant of the symmetric space
identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant
of symmetric space results.
If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it
can in principle be continued the p-adic context. One can however consider the possibility that
that the integrals over partonic 2-surfaces defining
ux Hamiltonians exist p-adically as Riemann
sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite
sub-manifold geometries in the discretized version of δM_{+}^{4}. If Kähler action is required
to exist p-adically same kind of condition applies to the space-time surfaces themselves. These
strong conditions might make sense in the intersection of the real and p-adic worlds assumed to
characterized living matter.

**Category:** Mathematical Physics

[17] **viXra:1006.0035 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 34 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first approach relies on a direct guess of Kähler function. Second
approach relies on the construction of Kähler form and metric utilizing the huge symmetries
of the geometry needed to guarantee the mathematical existence of Riemann connection. The
third approach discussed in this article relies on the construction of spinor structure based on the
hypothesis that complexified WCW gamma matrices are representable as linear combinations of
fermionic oscillator operator for the second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a
geometrization of fermionic statistics.
The basic philosophy is that at fundamental level the construction of WCW geometry reduces
to the second quantization of the induced spinor fields using Dirac action. This assumption
is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and
antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac
determinant and the conjecture is that it reduces to the exponent of Kähler function. In order
to achieve internal consistency induced gamma matrices appearing in Dirac operator must be
replaced by the modified gamma matrices defined uniquely by Kähler action and one must also
assume that extremals of Kähler action are in question so that the classical space-time dynamics
reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator
algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry
algebra different however from standard SUSY algebra in that Majorana spinors are
not needed. This algebra serves as a building brick of various super-conformal algebras involved.
The requirement that there exist deformations giving rise to conserved Noether charges requires
that the preferred extremals are critical in the sense that the second variation of the Kähler action
vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at
least involve it.
Quantum classical correspondence demands that quantum numbers are coded to the properties
of the preferred extremals given by the Dirac determinant and this requires a linear coupling
to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement
interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole
throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to
have physical propagators reducing to Dirac propagator not possible without the measurement
interaction term. An essential point is that the measurement interaction corresponds formally
to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form
of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the
effect of measurement interaction term to Kähler function reduces effectively to the same gauge
transformation.
The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at
the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric
spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW
Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part
between the ends. General expressions for the super-counterparts of WCW
ux Hamiltoniansand
for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis
of this picture.

**Category:** Mathematical Physics

[16] **viXra:1006.0034 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 26 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first one relies on a direct guess of Kähler function. Second approach
relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry
needed to guarantee the mathematical existence of Riemann connection. The third approach relies
on the construction of spinor structure assuming that complexified WCW gamma matrices are
representable as linear combinations of fermionic oscillator operator for the second quantized free
spinor fields at space-time surface and on the geometrization of super-conformal symmetries in
terms of spinor structure.
In this article the construction of Kähler form and metric based on symmetries is discussed.
The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with
lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy
ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality
and the basic objects are pairs partonic 2-surfaces X^{2} at opposite light-like boundaries of causal
diamonds (CDs).
The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric
spaces G/H labeled by zero modes having an interpretation as classical, non-quantum
uctuating
variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary
δM_{+}^{4}
+ and of light-like 3-surfaces implying a generalization of conformal invariance. The group
G acting as isometries of WCW is tentatively identified as the symplectic group of
δM_{+}^{4} x CP_{2}
localized with respect to X^{2}. H is identified as Kac-Moody type group associated with isometries
of H = M_{+}^{4} x CP_{2} acting on light-like 3-surfaces and thus on X^{2}.
An explicit construction for the Hamiltonians of WCW isometry algebra as so called
ux
Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of
these. Explicit expressions for WCW
ux Hamiltonians as functionals of complex coordinates of
the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic
2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are
proposed.

**Category:** Mathematical Physics

[15] **viXra:1006.0033 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 38 Pages.

There are two basic approaches to quantum TGD. The first approach, which is discussed in
this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional
context. Second approach is based on the identification of physics as a generalized
number theory. The first approach relies on the vision of quantum physics as infinite-dimensional
Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces
in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing
WCW Kähler geometry and spinor structure. The first approach relies on direct guess
of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing
the huge symmetries of the geometry needed to guarantee the mathematical existence of
Riemann connection. The third approach relies on the construction of spinor structure based on
the hypothesis that complexified WCW gamma matrices are representable as linear combinations
of fermionic oscillator operator for second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of WCW spinor structure.
In this article the proposal for Kähler function based on the requirement of 4-dimensional General
Coordinate Invariance implying that its definition must assign to a given 3-surface a unique
space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal
of some some general coordinate invariant action, and so called Kähler action is a unique
candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit
so that classical physics becomes and exact part of WCW geometry and therefore also quantum
physics.
The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions
lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of
causal diamond and with the light-like wormhole throats at which the signature of the induced
metric changes. The first assumption is the weak form of electric magnetic duality. Second
assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0
implying that the
ow parameter of the
ow lines of jK defines a global space-time coordinate.
This would mean that the vision about reduction to almost topological QFT would be realized.
Second challenge is the understanding of the space-time correlates of quantum criticality.
Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck
constant realized in terms of coverings of the imbedding space follows from basic quantum TGD
leads to a further understanding. The extreme non-linearity of canonical momentum densities as
functions of time derivatives of the imbedding space coordinates implies that the correspondence
between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP_{2}.
This leads also to a precise geometric characterization of the criticality of the preferred extremals.

**Category:** Mathematical Physics

[14] **viXra:1006.0032 [pdf]**
*submitted on 16 Jun 2010*

**Authors:** Matti Pitkänen

**Comments:** 32 Pages.

There are two basic approaches to the construction of quantum TGD. The first approach
relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of
classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially
a generalization of the Einstein's geometrization of physics program is in question. The second
vision is the identification of physics as a generalized number theory. This program involves
three threads: various p-adic physics and their fusion together with real number based physics
to a larger structure, the attempt to understand basic physics in terms of classical number fields
(in particular, identifying associativity condition as the basic dynamical principle), and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry
and generalized number theory are given to be followed by more detailed articles.

**Category:** Mathematical Physics

[13] **viXra:1003.0027 [pdf]**
*submitted on 6 Mar 2010*

**Authors:** Florentin Smarandache, V. Christianto, Fu Yuhua, Radi I. Khrapko, J. Hutchison

**Comments:** 147 pages

The reader will find herein a collection of unsolved problems in mathematics
and the physical sciences. Theoretical and experimental domains have each
been given consideration. The authors have taken a liberal approach in their
selection of problems and questions, and have not shied away from what
might otherwise be called speculative, in order to enhance the opportunities
for scientific discovery.
Progress and development in our knowledge of the structure, form and function
of the Universe, in the true sense of the word, its beauty and power, and
its timeless presence and mystery, before which even the greatest intellect is
awed and humbled, can spring forth only from an unshackled mind combined
with a willingness to imagine beyond the boundaries imposed by that
ossified authority by which science inevitably becomes, as history teaches
us, barren and decrepit.
Revealing the secrets of Nature, so that we truly see 'the sunlit plains extended,
and at night the wondrous glory of the everlasting stars', requires
far more than mere technical ability and mechanical dexterity learnt form
books and consensus. The dustbin of scientific history is replete with discredited
consensus and the grand reputations of erudite reactionaries. Only
by boldly asking questions, fearlessly, despite opposition, and searching for
answers where most have not looked for want of courage and independence
of thought, can one hope to discover for one's self. From nothing else can
creativity blossom and grow, and without which the garden of science can
only aspire to an overpopulation of weeds.

**Category:** Mathematical Physics

[12] **viXra:1001.0044 [pdf]**
*submitted on 28 Jan 2010*

**Authors:** Constantinos Ragazas

**Comments:** 8 pages

We derive a characterization of simple exponential functions that has the exact
mathematical form to Planck's Formula for blackbody radiation in Quantum Physics.

**Category:** Mathematical Physics

[11] **viXra:1001.0002 [pdf]**
*submitted on 6 Jan 2010*

**Authors:** Elemér E Rosinger

**Comments:** 17 pages.

A simple and rather general mathematical model of the phenomenon
of information is presented, followed by several examples and
comments.

**Category:** Mathematical Physics

[10] **viXra:0910.0069 [pdf]**
*submitted on 31 Oct 2009*

**Authors:** Vladimir I. Smirnov

**Comments:** 34 pages, Russian and English versions included

It is identified the new class of invariants which values are constant at change of value of an inde-pendent variable.
Their properties and a deriving method are shown on already known and still un-known instances, concerning to various
areas of physics. In particular, new invariants (50), (55) and (57) for the straight lines intersected in one point on
a plane have been discovered. Besides, the re-quest for detection of the third (not dependent on two already known) an
invariant (31) electromag-netic fields for a special case of the special theory of relativity is made.

**Category:** Mathematical Physics

[9] **viXra:0910.0016 [pdf]**
*submitted on 11 Oct 2009*

**Authors:** Chris Forbes

**Comments:** 10 pages

In this, a follow up to a previous paper 'A Short Article On A Newly
Proposed Model Of Cosmology' (viXra:0909.0005), some of the basic
mathematical structures to be used in the formulation of the model are
shown, and several advantages are discussed. The paper then takes a
more phenomenological approach and several simple (1+1) dimensional
models are explored.

**Category:** Mathematical Physics

[8] **viXra:0909.0026 [pdf]**
*submitted on 9 Sep 2009*

**Authors:** Bruce Rout

**Comments:** 13 pages

This paper examines the difference between infinite and finite domains
of a Stefan Problem. It is pointed out that attributes of solutions
to the Diffusion Equation suggest assumptions of an infinite domain
are invalid during initial times for finite domain Stefan Problems. The
paper provides a solution for initial and early times from an analytical
approach using a perturbation. This solution can then easily be applied
to numerical models for later times. The differences of the two domains
are examined and discussed.

**Category:** Mathematical Physics

[7] **viXra:0908.0045 [pdf]**
*submitted on 10 Aug 2009*

**Authors:** Hamid V. Ansari

**Comments:** 7 pages

It is shown that the wave equation cannot be solved for the general
spreading of the cylindrical wave using the method of separation of variables.
But an equation is presented in case of its solving the above act
will have occurred. Also using this equation the above-mentioned general
spreading of the cylindrical wave for large distances is obtained which
contrary to what is believed consists of arbitrary functions.

**Category:** Mathematical Physics

[6] **viXra:0908.0001 [pdf]**
*submitted on 1 Aug 2009*

**Authors:** Vladislav Konovalov

**Comments:** 12 pages

In the article the new calculuses are offered similar differential and integral, but differing,
that in them the analysis of the previous and subsequent values of a function is made. The
new calculuses allow to decide problems, the solution which one with usage customary
differential and integral calculus is impossible.

**Category:** Mathematical Physics

[5] **viXra:0907.0002 [pdf]**
*submitted on 9 Jul 2009*

**Authors:** Philip Gibbs

**Comments:** 5 pages, published in Prespacetime Journal, V5

We prove that any 3x3 unitary matrix can be transformed to a magic matrix by multiplying its rows
and columns by phase factors. A magic matrix is defined as one for which the sum of the elements in any row
or column add to the same value. This result is relevant to recent observations on particle mixing matrices.

**Category:** Mathematical Physics

[4] **viXra:0812.0008 [pdf]**
*submitted on 21 Dec 2008*

**Authors:** R. M. Kiehn

**Comments:** recovered from sciprint.org

Finally, I have found time to think about, and the incentive to study, how the
field theory of Topological thermodynamics, electrodynamics, and hydrodynamics
can be compared to field theory concepts that have been developed by Lagrangian
methods, for both the classic and quantum mechanical varieties. For more than
30 years I have known that Cartan's topological methods could be applied to
dissipative systems; the methods based on diffeomorphic-invariant Lagrangian
field theories can not. The incentive came when I realized that the topological
methods of Cartan gave dynamical results that can explain "symmetry breaking"
and quantization in terms of continuous topological evolution.

**Category:** Mathematical Physics

[3] **viXra:0703.0022 [pdf]**
*submitted on 25 Mar 2007*

**Authors:** Carlos Castro

**Comments:** recovered from sciprint.org

A novel Chern-Simons E8 gauge theory of Gravity in D = 15 based on an octic E8 invariant expression
in D = 16 (recently constructed by Cederwall and Palmkvist) is developed. A grand unification model of
gravity with the other forces is very plausible within the framework of a supersymmetric extension (to
incorporate spacetime fermions) of this Chern-Simons E8 gauge theory. We review the construction showing
why the ordinary 11D Chern-Simons Gravity theory (based on the Anti de Sitter group) can be embedded
into a Clifford-algebra valued gauge theory and that an E8 Yang-Mills field theory is a small sector of a
Clifford (16) algebra gauge theory. An E8 gauge bundle formulation was instrumental in the understanding
the topological part of the 11-dim M-theory partition function. The nature of this 11-dim E8 gauge theory
remains unknown. We hope that the Chern-Simons E8 gauge theory of Gravity in D = 15 advanced in this
work may shed some light into solving this problem after a dimensional reduction.

**Category:** Mathematical Physics

[2] **viXra:0703.0021 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** Fu Yuhua

**Comments:** recovered from sciprint.org

Discussing the applications of Dynamic Smarandache Multi-Space (DSMS)
Theory. Supposing for the n different dynamic spaces (n is a dynamic positive integer and
the function of time) the different equations have been established, as these n different
dynamic spaces synthesize the DSMS, and they are mutually affected, some new coupled
equations need to establish in the DSMS to replace some equations in the original dynamic
spaces, as well as supply other equations to process the contact, boundary conditions and
so on. For the unified processing of all equations in the DSMS, this paper proposes to run
the quantization processing to all the variables and all the equations and establish the
unified variational principle of quantization with the collocation method based on the
method of weighted residuals, and simultaneously solve all the equations in the DSMS with
the optimization method. Thus by using the unified variational principle of quantization in
the DSMS and the fractal quantization method, will pave the way for the unified processing
of the theory of relativity and the quantum mechanics, and the unified processing of the
four foundational interactions. Finally the coupled solution for the problem of relativity and
quantum mechanics is discussed.

**Category:** Mathematical Physics

[1] **viXra:0703.0020 [pdf]**
*submitted on 18 Mar 2007*

**Authors:** Mircea Eugen Selariu

**Comments:** recovered from sciprint.org

The discovery of mathematical complements, assembled under the name of the eccentric mathematics, gave the opportunity
for a series of applications, amongst which, in this article, are presented the impulse, step, and unitary ramp functions. The difference,
in comparison with the same classic functions, from the distributions theory, is that those eccentric are periodical with a 2π period. By
combining these between them, new mathematical functions have been defined; united under the name Smarandache stepped
functions.

**Category:** Mathematical Physics

[171] **viXra:1404.0280 [pdf]**
*replaced on 2014-04-18 17:39:32*

**Authors:** Koji Sugiyama

**Comments:** 16 Pages.

This paper converges the sum of all natural numbers by damped oscillation summation method of a new zeta function regularization.

The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converge by the regularization. It diverges. This paper converges the sum by damped oscillation summation method of the new regularization.

It is desirable that both the integral representation and the series representation have a same value for mathematical consistency. One method to converge the divergent series is Abel summation method. The method converges the divergent series by multiplying convergence factor. However, the sum of all natural numbers does not converge by the method. Therefore, it is an important issue to find a new summation method.

We define a new "sum of all natural numbers" by a new summation method, damped oscillation summation method. The method converges the divergent series by multiplying convergence factor, which is damped and oscillating very slowly. The traditional sum diverges for the infinite terms. On the other hand, the new "sum" is equal to the traditional sum for the finite term. In addition, the "sum" converges on -1/12 for the infinite term.

**Category:** Mathematical Physics

[170] **viXra:1404.0280 [pdf]**
*replaced on 2014-04-17 12:12:04*

**Authors:** Koji Sugiyama

**Comments:** 16 Pages.

This paper converges all natural numbers by damped oscillation summation method of a new zeta function regularization.

The zeta function regularization is a method to assign finite values to divergent integration or sums. One method of the regularization is the analytic continuation. The integral representation of the zeta function converges by the analytic continuation. On the other hand, the zeta function also has a series representation. One of the representation is the sum of all natural numbers. The sum does not converges by the regularization. It diverges. This paper converges the sum by damped oscillation summation method of the new regularization.

It is desirable that both the integral representation and the series representation have same value for mathematical consistency. One method to converge the divergent series is Abel summation method. The method converge the divergent series by multiplying convergence factor. However, the sum of all natural numbers does not converge by the method. Therefore it is an important issue to find a new summation method.

We define new "sum of all natural numbers" by new summation method, damped oscillation summation method. The method converge the divergent series by multiplying convergence factor which is damped and oscillating very slowly. The traditional sum diverges for infinite terms. On the other hand, the new "sum" equals the traditional sum for the finite term. And the "sum" converges on -1/12 for the infinite term.

**Category:** Mathematical Physics

[169] **viXra:1403.0042 [pdf]**
*replaced on 2014-03-22 09:40:55*

**Authors:** Giuseppe Rauti

**Comments:** 1 Page.

Dynamical System Theory and Chaos Theory.

**Category:** Mathematical Physics

[168] **viXra:1402.0151 [pdf]**
*replaced on 2014-02-23 14:37:53*

**Authors:** William O. Straub

**Comments:** 7 Pages. A few minor revisions

In a series of papers written over the period 1944-1948, the great Austrian physicist Erwin Schrödinger presented his ideas on symmetric and non-symmetric affine connections and their possible application to general relativity. Several of these ideas were subsequently presented in his notable 1950 book "Space-Time Structure," in which Schrödinger outlined the case for both metric and general connections, symmetric and otherwise. In the following discussion we focus on one particular connection presented by Schrödinger in that book and its relationship with the non-metricity tensor. We also discuss how this connection overcomes a problem that Hermann Weyl experienced with the connection he proposed in his failed 1918 theory
of the combined gravitational-electromagnetic field. A simple physical argument is then presented demonstrating that Schrödingers’s formalism accommodates electromagnetism in a more natural way than Weyl’s theory.

**Category:** Mathematical Physics

[167] **viXra:1402.0141 [pdf]**
*replaced on 2014-02-27 22:32:06*

**Authors:** A. A. Frempong

**Comments:** 24 Pages.

"Since a picture is worth a thousand words, a solution to the Navier-Stokes equations is worth a thousand proofs of the existence of the solutions of the Navier-Stokes equations"--Application proverb.
This paper covers analytic solutions of the 3-D linearized Navier-Stokes equations, solutions
of the Euler equations of fluid mechanics, and pending solutions of the non-linearized
Navier-Stokes equations. The nine term x-direction Navier-Stokes equation was linearized to a
six-term equation. For this linearized equation, different terms of the equation were made subjects of the equation, and each such equation was integrated by first splitting-up the equation (using a multiplier method) into sub-equations, solving each sub-equation, and then combining the integration results. A total of twenty sub-equations were solved. The relations obtained using different terms as subjects of the equations were checked in the corresponding linearized equations. Only the equation with the gravity term, g, as the subject of the equation satisfied
its corresponding equation. However, all the integrals obtained for the four different subjects revealed the role of each term in fluid flow. In particular, the gravity forces are involved mainly in the parabolic and the forward motion of fluids. Similarly as above, the Euler equation in
the x-direction was integrated using the multiplier method and using the gravity term g, as the subject of the equation. The integration results satisfied the corresponding Euler equation. For the non-linearized Navier-Stokes equation, the results of the linearized equation were continued by adding three more integrals from the non-linear terms of the Euler solution and adjusting the coefficient of the linear acceleration term. To obtain an identity for the non-linearized Navier-Stokes equation, the linear part of the integration results was checked against the linear part of the equation; and the non-linear part of the integration results was checked against the non-linear part of the equation. The integration results using the above checking method satisfied the Navier-Stokes equation. Other topics covered include the applications of the splitting technique and its results in science, engineering, economics and business fields. For a spin-off, the solutions from above were specialized to satisfy the requirements of the CMI Millennium Prize Problem, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[166] **viXra:1402.0141 [pdf]**
*replaced on 2014-02-26 22:39:35*

**Authors:** A. A. Frempong

**Comments:** 24 Pages.

"Since a picture is worth a thousand words, a solution to the Navier-Stokes equations is worth a thousand proofs of the existence of the solutions of the Navier-Stokes equations"--Application proverb.
This paper covers analytic solutions of the 3-D linearized Navier-Stokes equations, solutions
of the Euler equations of fluid mechanics, and pending solutions of the non-linearized
Navier-Stokes equations. The nine term x-direction Navier-Stokes equation was linearized to a
six-term equation. For this linearized equation, different terms of the equation were made subjects of the equation, and each such equation was integrated by first splitting-up the equation (using a multiplier method) into sub-equations, solving each sub-equation, and then combining the integration results. A total of twenty sub-equations were solved. The relations obtained using different terms as subjects of the equations were checked in the corresponding linearized equations. Only the equation with the gravity term, g, as the subject of the equation satisfied
its corresponding equation. However, all the integrals obtained for the four different subjects revealed the role of each term in fluid flow. In particular, the gravity forces are involved mainly in the parabolic and the forward motion of fluids. Similarly as above, the Euler equation in
the x-direction was integrated using the multiplier method and using the gravity term g, as the subject of the equation. The integration results satisfied the corresponding Euler equation. For the non-linearized Navier-Stokes equation, the results of the linearized equation were continued by adding three more integrals from the non-linear terms of the Euler solution and adjusting the coefficient of the linear acceleration term. To obtain an identity for the non-linearized Navier-Stokes equation, the linear part of the integration results was checked against the linear part of the equation; and the non-linear part of the integration results was checked against the non-linear part of the equation. The integration results using the above checking method satisfied the Navier-Stokes equation. Other topics covered include the applications of the splitting technique and its results in science, engineering, economics and business fields. For a spin-off, the solutions from above were specialized to satisfy the requirements of the CMI Millennium Prize Problem, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[165] **viXra:1402.0141 [pdf]**
*replaced on 2014-02-22 23:14:07*

**Authors:** A. A. Frempong

**Comments:** 24 Pages.

"Since a picture is worth a thousand words, a solution to the Navier-Stokes equations is worth a thousand proofs of the existence of the solutions of the Navier-Stokes equations"--Application proverb.
This paper covers analytic solutions of the 3-D linearized Navier-Stokes equations, solutions
of the Euler equations of fluid mechanics, and pending solutions of the non-linearized
Navier-Stokes equations. The nine term x-direction Navier-Stokes equation was linearized to a
six-term equation. For this linearized equation, different terms of the equation were made subjects of the equation, and each such equation was integrated by first splitting-up the equation (using a multiplier method) into sub-equations, solving each sub-equation, and then combining the integration results. A total of twenty sub-equations were solved. The relations obtained using different terms as subjects of the equations were checked in the corresponding linearized equations. Only the equation with the gravity term, g, as the subject of the equation satisfied
its corresponding equation. However, all the integrals obtained for the four different subjects revealed the role of each term in fluid flow. In particular, the gravity forces are involved mainly in the parabolic and the forward motion of fluids. Similarly as above, the Euler equation in
the x-direction was integrated using the multiplier method and using the gravity term g, as the subject of the equation. The integration results satisfied the corresponding Euler equation. For the non-linearized Navier-Stokes equation, the results of the linearized equation were continued by adding three more integrals from the non-linear terms of the Euler solution and adjusting the coefficient of the linear acceleration term. To obtain an identity for the non-linearized Navier-Stokes equation, the linear part of the integration results was checked against the linear part of the equation; and the non-linear part of the integration results was checked against the non-linear part of the equation. The integration results using the above checking method satisfied the Navier-Stokes equation. Other topics covered include the applications of the splitting technique and its results in science, engineering, economics and business fields. For a spin-off, the solutions from above were specialized to satisfy the requirements of the CMI Millennium Prize Problem, and thus prove the existence of smooth solutions of the Navier-Stokes equations.

**Category:** Mathematical Physics

[164] **viXra:1402.0050 [pdf]**
*replaced on 2014-02-23 14:13:30*

**Authors:** J. S. Markovitch

**Comments:** 3 Pages.

A special case of the cubic equation, distinguished by having an unusually economical solution, is shown to relate to both the fine structure constant inverse (approximately 137.036) and the sines squared of the quark and lepton mixing angles.

**Category:** Mathematical Physics

[163] **viXra:1401.0215 [pdf]**
*replaced on 2014-04-04 09:00:16*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 31 Pages.

After the concept of a locally scale-invariant spacetime has been introduced in the companion document, now physical experiments on mathematical entities will be performed to find out implications of that model.
With regard to earlier solutions by others, an unbiased inspection of different gravitational scenarios under local scale-invariance in comparison with physical reality is undertaken.
This gives five results at once: A suspected locality condition, a promising gravitational ansatz, a static solution for the gravitational potential in the subjective picture together with a possible static cosmic redshift, and a set of candidate terms for governing field equations of physical spacetime.

**Category:** Mathematical Physics

[162] **viXra:1401.0153 [pdf]**
*replaced on 2014-03-08 11:44:52*

**Authors:** Nicolas Poupart

**Comments:** 8 Pages.

This paper presents a theory of the relativistic gravitational field by simply applying Carnot's principle to the gravitation and by reinforcing as inviolable the mass-energy equivalence law and the equivalence of the inertial mass and the heavy mass. It will be shown that this theory can explain easily the origin of dark matter and dark energy. In addition, it will also be shown that this theory is not distinguishable from general relativity at our experimental scale.

**Category:** Mathematical Physics

[161] **viXra:1401.0152 [pdf]**
*replaced on 2014-03-08 11:47:40*

**Authors:** Nicolas Poupart

**Comments:** 8 Pages.

Cet article expose une théorie du champ gravitationnel relativiste en appliquant simplement le principe de Carnot à la gravitation et en considérant la loi d'équivalence masse-énergie ainsi que l'équivalence masse inertielle et masse pesante comme inviolable. Il sera démontré que cette théorie permet d'expliquer aisément l'origine de la matière noire ainsi que de l'énergie noire. De plus, il sera également démontré que cette théorie n'est pas différenciable de la relativité générale à notre échelle expérimentale.

**Category:** Mathematical Physics

[160] **viXra:1401.0145 [pdf]**
*replaced on 2014-01-26 07:38:30*

**Authors:** Dan Visser

**Comments:** 5 Pages. I hope Peter Coles University of Sussex UK takes notice, as well as the media.

The Universe rotates. We live in a Double Torus Universe. A dark matter torus rotates in a larger time torus of refined time smaller than the Planck-time. The Planck-satellite showed a more detailed picture of the CMB related to Big Bang cosmology. However, I have put that in perspective of a new set of equations that belong to the framework of the Double Torus Theory. That shows my proof for a rotational dark matter Flow by warm and cold areas in the CMB. I also explain why the accelerated space-expansion in the Big Bang cosmology is an illusion.

**Category:** Mathematical Physics

[159] **viXra:1401.0107 [pdf]**
*replaced on 2014-04-13 13:43:39*

**Authors:** Dan Visser

**Comments:** 9 Pages.

Fly-By- and GPS-satellites reveal an earth-dark matter-halo is affecting the orbit-velocities of satellites. After analysis by a new set of equations, which describe dark matter, dark matter-force and quantum-gravity combined in a new dark energy force-formula, the new formulations match a percentage whereof satellites feel extra gravity. Also the dark matter-density has been calculated. The analysis confirms dark matter exists as a halo around the earth. Secondly it shows what dark matter really is. It also shows what a dark flow is. The dark matter-features are presented in a Double Torus Cosmology, a new model for the universe, which replaces Big Bang cosmology and enables to understand dark matter better!

**Category:** Mathematical Physics

[158] **viXra:1312.0164 [pdf]**
*replaced on 2014-01-21 16:42:35*

**Authors:** Thierry PERIAT

**Comments:** 21 Pages.

Previous explorations have proposed a plausible and totally new path unifying the generalized theory of relativity and the quantum theory. It yields a specific expression for the EM field tensor. The aim of that new chapter is to understand the meaning of that formalism. I insist on a possible link with the notion of bi-vector exposed by E. Cartan. That v3 comes to the conclusion that that formalism sometimes represents an infinitesimal variation of the 4D metric.

**Category:** Mathematical Physics

[157] **viXra:1311.0196 [pdf]**
*replaced on 2013-11-30 09:17:51*

**Authors:** S.C. Gaudie

**Comments:** 11 pages; mostly font 11; A4 paper; UK English; Freelance scientist.

This answers fundamental questions from Wikipedia about Generations of Matter [**web 1] and related properties.
Why are there three generations of quarks and leptons? Why are the ratios of masses of quarks and leptons as they are?
Also, is the ratio of fundamental force strengths related to the size of the universe and why are the ratios as they are?
This theory defines a “fundamental sub-structure" that is a tetrahedron with the further “sub-structure" of spheres.
Another geometrical possibility, with the same values, is based on the spatial axes.
The big picture could be the arrangement of the “fundamental spheres” along the axes of space.
There seems to be a “universal template” for the properties of the universe. The ratio numbers can be thought of as "quantum numbers". The ratios for each of these “fundamental sub-structure", “quantum numbers” are 1, 3 & 6; simple integer values. The 1, 3, 6 “quantum numbers” ratios in this theory show why the relative masses & radii of quarks and the “heavy leptons” are their “known values”. The cube root of the mass was used to calculate a diameter ratio parameter for these. These ratios are also applied to other basic properties of the universe. This “fundamental sub-structure" has also been applied to the relative strengths of the fundamental forces determining the size of the universe at the time of their creation.
The universe is believed to have gone through creation of forces, inflation stages & must, of necessity, have gone through “phase changes". These could be interconnected.
This theory combines the above items into ONE overall theory. Unexpected conclusions of the theory is
[1] that gravity (like the nuclear force holding protons and neutrons together) is just another aspect of the strong nuclear force. This would mean that gravity works without gravitinos as force carriers or gavity waves! It also ties the force of gravity to its interaction with space!
[2] Mass is an ATTRACTION ONLY “CHARGE”! [No repulsive gravity = dark energy.]
[3] This gives numerical values to different inflation stages.
[My unpublished work:- accelerated expansion = “localised view” of start of a new inflation period! Natural evolution of the universe!]

**Category:** Mathematical Physics

[156] **viXra:1311.0189 [pdf]**
*replaced on 2013-12-15 09:13:30*

**Authors:** Dan visser

**Comments:** 5 Pages. I hope the press takes notice. The result violates GRT. Signed: Dan Visser, Almere, the Netherlands

In particular calculations have been made for the detection of extraterrestrial high energy neutrinos. Additional the rest-energy of a neutrino is calculated (equivalent to its rest mass). But both calculations are not standard. The calculations are made from the perspective of a new model for the universe: The Double Torus hypothesis. The alternative calculation shows that the result matches a neutrino-incident in the ICECUBE-project in Antartica for a value of 250 TeV energy. Moreover, an extra calculation is made for the expected neutrino rest-energy by the Standard Model (equivalent for its rest-mass). This shows time 21 times smaller than the Planck-time can generate a neutrino-rest-energy of 2.2 eV. It also shows time 100 times smaller than the Planck-time can generate a neutrino-rest-energy of 0.1 eV. This delivers evidence for the existence of a sub-quantum-domain of refined time that affects dark vacuum-particles; this is dark matter described in the Double Torus-framework. That generates visible quantum-gravitational particles. Such a calculation could also be performed for an electron or a quark. But that is not (yet) performed in this paper. But one of the conclusions is that the detection of high energy neutrinos could turn out to be additional evidence for the existence of rotational Double Torus Universe.

**Category:** Mathematical Physics

[155] **viXra:1311.0182 [pdf]**
*replaced on 2014-02-23 04:16:59*

**Authors:** Claude Michael Cassano

**Comments:** 16 Pages.

All the fermion masses may be determined from merely two numbers dependent on π , e , and a few rational fractions, and all the fermion charges thereafter., In this, now, dimension independent revision; the electron mass and the ratio of the muon mass to the electron mass are shown calculable from simple quadratic functions of π , e , and a few rational fractions. All the remaining masses may be determined from from these constants and their indexes determined by the mass-generalized Maxwell's equations. These calculated masses are all well within current specs as of this publication. In fact, more recent neutrino measurements and estimates have put their values into a rather tight range which the computed values in this update fall within.

**Category:** Mathematical Physics

[154] **viXra:1311.0170 [pdf]**
*replaced on 2013-11-28 14:20:49*

**Authors:** Sergey V. Ershkov

**Comments:** 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time.
In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids).
Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is proved to be ideal (unviscid) due to zero Laplacian.

**Category:** Mathematical Physics

[153] **viXra:1311.0170 [pdf]**
*replaced on 2013-11-27 01:35:23*

**Authors:** Sergey V. Ershkov

**Comments:** 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time.
In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids).
Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian.

**Category:** Mathematical Physics

[152] **viXra:1311.0170 [pdf]**
*replaced on 2013-11-26 08:50:02*

**Authors:** Sergey V. Ershkov

**Comments:** 6 Pages. Keywords: Helmholtz paradox, constant vortex, incompressible ideal flow

The reverse side of Helmholtz paradox is presented here. Helmholtz paradox itself had been formulated as follows: - in the ideal (non-viscid) newtonian fluids any vorticity should be stable (constant) during infinite time. It means that if vortex arise in non-viscid newtonian fluid, such a vortex should have the constant strength all the time.
In our note to Helmholtz paradox, we proved that Vortex with constant angular velocity of rotation could be generated only by the flow with zero Laplacian (thus, such a flow is not viscid for the case of incompressible newtonian fluids).
Thus, we could conclude in addition to Helmholtz paradox: not only any vortex should be constant in the ideal (non-viscid) newtonian fluids, but if vortex is constant it means that such a flow is turned to be ideal (unviscid) due to zero Laplacian.

**Category:** Mathematical Physics

[151] **viXra:1311.0164 [pdf]**
*replaced on 2014-02-20 09:01:31*

**Authors:** Algirdas Antano Maknickas

**Comments:** 8 Pages.

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 2D and 3D space for any shaped boundary was expressed in term of 2D and 3D global solution of Helmholtz equation accordantly.

**Category:** Mathematical Physics

[150] **viXra:1311.0164 [pdf]**
*replaced on 2014-02-14 01:07:23*

**Authors:** Algirdas Antano Maknickas

**Comments:** 7 Pages.

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly.

**Category:** Mathematical Physics

[149] **viXra:1311.0164 [pdf]**
*replaced on 2014-02-03 14:13:08*

**Authors:** Algirdas Antano Maknickas

**Comments:** 7 Pages.

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly.

**Category:** Mathematical Physics

[148] **viXra:1311.0164 [pdf]**
*replaced on 2013-12-06 03:44:14*

**Authors:** Algirdas Antano Maknickas

**Comments:** 6 Pages.

The fluid equations, named after Claude-Louis Navier and George Gabriel Stokes, describe the motion of fluid substances. These equations arise from applying Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term - hence describing viscous flow. Due to specific of NS equations they could be transformed to full/partial inhomogeneous parabolic differential equations: differential equations in respect of space variables and the full differential equation in respect of time variable and time dependent inhomogeneous part. Finally, orthogonal polynomials as the partial solutions of obtained Helmholtz equations were used for derivation of analytical solution of incompressible fluid equations in 1D, 2D and 3D space for rectangular boundary. Solution in 3D space for any shaped boundary is expressed in term of 3D global solution of 3D Helmholtz equation accordantly.

**Category:** Mathematical Physics

[147] **viXra:1311.0102 [pdf]**
*replaced on 2013-11-15 19:44:37*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 7 Pages.

The Wave Metric Theory (WMT), recently introduced by this author in [4], was discussed here in a more direct and simple way as an introduction to many who had never heard this approach to Unification Problem.

**Category:** Mathematical Physics

[146] **viXra:1311.0085 [pdf]**
*replaced on 2013-12-09 19:30:13*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 3 Pages. In Commemoration of the 11th Year Anniversary of Perelman's Posting of His First Paper on the use of Ricci Flow to Solve Poincare's Conjencture.

We further elaborated the Wave Metric Theory as a unification theory by giving emphasis on one of its assertions: the "Hierarchy of Metrics" that exists in Nature . We showed that there are three levels in the hierarchy and all can be described by a unified evolution equation.

**Category:** Mathematical Physics

[145] **viXra:1311.0001 [pdf]**
*replaced on 2013-11-02 20:42:02*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 18 Pages.

An alternative quantum interpretation was presented based on recent papers [1],[2] on a kind of metric theory that could possibly describes the so--called “quantum geometrodynamics”. It is shown that the spacetime in which its metric is continuously fluctuating serves as a “sub-quantum medium” that guides the quantum particles. It is shown that the conventional quantum mechanics can be derived as a low-energy approximation from a fundamental metric theory at subquantum level (SQL) with a generalized Lorentz Invariance and an energy-dependent Planck’s “constant”. Lastly, it is shown that nonlocality can be cosmological in origin.

**Category:** Mathematical Physics

[144] **viXra:1311.0001 [pdf]**
*replaced on 2013-11-01 21:08:03*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 18 Pages.

An alternative quantum interpretation was presented based on recent papers[1],[2] on a kind of metric theory that could possibly describes the so--called “quantum geometrodynamics”. It is shown that the spacetime in which its metric is continuously fluctuating serves as a “sub-quantum medium” that guides the quantum particles. It is shown that the conventional quantum mechanics can be derived as a low-energy approximation from a fundamental metric theory at subquantum level (SQL) with a generalized Lorentz Invariance and an energy-dependent Planck’s “constant”. Lastly, it is shown that nonlocality can be cosmological in origin.

**Category:** Mathematical Physics

[143] **viXra:1310.0235 [pdf]**
*replaced on 2014-04-04 09:01:45*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 20 Pages.

A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor.
The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined.

**Category:** Mathematical Physics

[142] **viXra:1310.0235 [pdf]**
*replaced on 2013-11-24 10:47:46*

**Authors:** Carsten S.P. Spanheimer

**Comments:** 20 Pages.

A framework for calculations in a semi-Riemannian space with the typical metric connection and curvature expressions is developed, with an emphasis on deriving them from an embedding function as a more fundamental object than the metric tensor. The scale-invariant and 'linearizing' logarithmic nature of an 'infinitesimal embedding' of a tangent space into its neighbourhood is observed, and a composition scheme of spacetime scenarios from 'outer' non-invariant and 'inner' scale-invariant embeddings is briefly outlined.

**Category:** Mathematical Physics

[141] **viXra:1310.0210 [pdf]**
*replaced on 2013-10-29 01:33:49*

**Authors:** Jeffrey Alloy Q. Abanto

**Comments:** 9 Pages.

We presented an alternative spacetime number though limited in nature which we called as Implex Number. It is different from other well-known spacetime number called in various names such as: Split-Complex Number, Hyperbolic Number and Perplex Numbers. It is a valid extension of the Real Number System along with the Complex Number System and Perplex Number System. It is shown in 2-D the algebra at once is non-Abelian, non-associative and chiral under the multiplication operation. Finally we suggest that it can be used as a basis for a non-commutative geometry and for a deformation of Lorentz Invariance.

**Category:** Mathematical Physics

[140] **viXra:1310.0191 [pdf]**
*replaced on 2014-04-17 10:16:12*

**Authors:** Malcolm Macleod

**Comments:** 4 Pages.

In this essay I look at a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, (Planck) time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant to 0.101373253 x $10^{-124}$ units of Planck time. Results for the universe mass density, the cosmic radiation energy density and the cosmic microwave background temperature correspond with observed.

**Category:** Mathematical Physics

[139] **viXra:1310.0191 [pdf]**
*replaced on 2014-04-10 07:06:38*

**Authors:** Malcolm Macleod

**Comments:** 3 Pages.

In this essay I look at a simple rotating expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole universe to the black-hole universe thereby giving a simple rationale for the expansion of the universe, (Planck) time, the arrow of time, the speed of light, dark energy, dark matter and the Stefan Boltzmann constant. A discrete unit of temperature is suggested and this is used to solve the cosmological constant to 0.101373253 x $10^{-124}$ units of Planck time. Results for the universe mass density, the cosmic radiation energy density and the cosmic microwave background temperature correspond with observed.

**Category:** Mathematical Physics

[138] **viXra:1310.0191 [pdf]**
*replaced on 2014-03-18 11:01:26*

**Authors:** Malcolm Macleod

**Comments:** 2 Pages.

In this essay I look at an expanding black-hole universe with a contracting white-hole universe twin. Units of Planck momentum are transferred in discrete integer steps from the white-hole to the black-hole thereby giving a simple rationale for the expansion of the universe, time, the arrow of time, the speed of light, dark energy and dark matter.

**Category:** Mathematical Physics

[137] **viXra:1310.0191 [pdf]**
*replaced on 2014-02-23 04:25:14*

**Authors:** Malcolm Macleod

**Comments:** 2 Pages.

In this essay I propose an expanding black-hole universe (ours) with a contracting white-hole universe twin. Units of Planck momentum are transferred discretely from the white-hole to the black-hole thereby giving a rationale for the expansion of the universe, time, the arrow of time, dark energy and dark matter.

**Category:** Mathematical Physics

[136] **viXra:1310.0082 [pdf]**
*replaced on 2013-12-05 01:12:07*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here.
We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one.
The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function).
As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.

**Category:** Mathematical Physics

[135] **viXra:1310.0082 [pdf]**
*replaced on 2013-10-18 09:46:36*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here.
We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one.
The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function).
As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.

**Category:** Mathematical Physics

[134] **viXra:1310.0082 [pdf]**
*replaced on 2013-10-15 12:32:05*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here.
We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one.
The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function).
As for solenoidal (divergence-free) equation, the transition from Cartesian to curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.

**Category:** Mathematical Physics

[133] **viXra:1310.0082 [pdf]**
*replaced on 2013-10-14 05:20:56*

**Authors:** Sergey V. Ershkov

**Comments:** 7 Pages. Keywords: Navier-Stokes equations, self-similar solutions, incompressible flow

A new classification of self-similar solutions of the Navier-Stokes system of equations is presented here.
We consider equations of motion for incompressible flow (of Newtonian fluids) in the curl rotating co-ordinate system. Then the equation of momentum should be split into the sub-system of 2 equations: an irrotational (curl-free) one, and a solenoidal (divergence-free) one.
The irrotational (curl-free) equation used for obtaining of the components of pressure gradient. As a term of such an equation, we used the irrotational (curl-free) vector field of flow velocity, which is given by the proper potential (besides, the continuity equation determines such a potential as a harmonic function).
As for solenoidal (divergence-free) equation, transition from Cartesian to the the curl rotating co-ordinate system transforms equation of motion to the Helmholtz vector differential equation for time-dependent self-similar solutions. The Helmholtz differential equation can be solved by separation of variables in only 11 coordinate systems, so it forms a complete set of all possible cases of self-similar solutions for Navier-Stokes system of equations.

**Category:** Mathematical Physics

[132] **viXra:1309.0087 [pdf]**
*replaced on 2013-09-14 21:55:02*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 10 Pages.

The following article briefly lays out a plausible alternative to the P=NP problem, and defines a general physical approach to the computational physics involved. It makes a conjecture that the underlying differences between quantum systems and classical mechanics can be bridged by a newer and novel mathematical parameter.

**Category:** Mathematical Physics

[131] **viXra:1308.0140 [pdf]**
*replaced on 2014-03-28 04:07:37*

**Authors:** Malcolm Macleod

**Comments:** 8 Pages.

In this essay I propose an alternate interpretation whereby particles may be linked, not by the 4 forces, but by orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons or orbitons) that are trapped to form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals (orbitons), the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different $g$), then we will change its orbital mass. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational reduces to $E_{orbital} = E_{Planck}/(2.\alpha)$.

**Category:** Mathematical Physics

[130] **viXra:1308.0140 [pdf]**
*replaced on 2014-02-23 08:42:44*

**Authors:** Malcolm Macleod

**Comments:** 8 Pages.

In this essay I propose an alternate interpretation whereby particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals, the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different $g$), then we will change its relativistic mass. Total momentum appears to derive from the classical orbital momentum, an orbital rotational momentum and a spin momentum. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational reduces to $E_{orbital} = E_{Planck}/(2.\alpha)$.

**Category:** Mathematical Physics

[129] **viXra:1308.0140 [pdf]**
*replaced on 2013-11-14 22:00:53*

**Authors:** Malcolm Macleod

**Comments:** 8 Pages.

In this essay, I propose that particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves. For example, gravitational orbits would be the sum of these gravitational orbitals, the moon is not orbiting the earth, rather it is being propelled by these orbital momenta. Likewise there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in mass density (buoyancy). As such, if we move the IPK 1kg reference bar to a different location (with a different $g$), then we will change its mass. Total momentum derives from the classical orbital momentum, an orbital rotational momentum and a spin momentum. The fundamental unit of orbital energy, whether nuclear, atomic, molecular or gravitational is E_{orbital} = E_{Planck}/(2*alpha).

**Category:** Mathematical Physics

[128] **viXra:1308.0140 [pdf]**
*replaced on 2013-10-27 16:12:01*

**Authors:** Malcolm Macleod

**Comments:** 7 Pages.

In this essay I propose that particles may be linked, not by the 4 forces, but by physical orbitals; that nuclear, atomic, molecular and gravitational orbital wave-functions are actually physical entities, photons albeit of inverse phase (anti-photons) that form standing waves, and so gravitational orbits then become the sum of these gravitational orbitals, the moon for example, does not orbit the earth, rather it is propelled by this orbital momentum. The orbital frequency is a function of the respective particle frequencies with a relativistic spin-momentum velocity correction. Consequently there is no empty space within the atom or nucleus, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in buoyancy. As such, if we move the IPK 1kg reference bar to a different location (with a different $g$), then we will change its mass.

**Category:** Mathematical Physics

[127] **viXra:1308.0140 [pdf]**
*replaced on 2013-10-23 02:55:51*

**Authors:** Malcolm Macleod

**Comments:** 7 Pages.

In this essay I propose that particles may be linked, not by the 4 forces, but by physical orbitals; photons albeit of inverse phase (anti-photons) that form standing waves. Gravitational orbits then become the sum of gravitational orbitals, the moon for example, does not orbit the earth, rather it is propelled by this orbital momentum. The orbital frequency is a function of the respective particle frequencies with a relativistic spin-momentum velocity correction. Consequently there is no empty space within the atom, instead particles are 'quantumly entangled' via these physical anti-photon orbital links. As orbitals have different energy densities, movement between orbitals requires a change in buoyancy. As such, if we move the IPK 1kg reference bar to a different location (with a different $g$), then we will change its mass.

**Category:** Mathematical Physics

[126] **viXra:1308.0125 [pdf]**
*replaced on 2014-04-14 07:44:18*

**Authors:** Robert A. Herrmann

**Comments:** 34 Pages.

This article develops and employs modern methods for mathematical modeling. This version uses these techniques to continue the development of useful refinements. In particular, the methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from observable entities and processes that are employed to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-world-like object such that when an hyper-algorithm, is applied to it and ultra-logic-system is hyper-deduced. Another application of the hyper-algorithm yields an hyperfinite instruction paradigm that is hyper-deduced in the required order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patton and Wheeler participator universe requirements. A specific physical data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. The set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields, all physical and physical-like systems are produced.

**Category:** Mathematical Physics

[125] **viXra:1308.0125 [pdf]**
*replaced on 2014-03-03 07:32:39*

**Authors:** Robert A. Herrmann

**Comments:** 34 Pages.

This article develops and employs modern methods for mathematical modeling. This version uses these techniques to continue the development of useful refinements. In particular, the methods of nonstandard analysis are applied to general language logic-systems. This allows the operators for the only known mathematical cosmogony, the General Grand Unification Model (GGU-Model), to more clearly exhibit their hyper-logical properties. All of the GGU-model entities and processes are predicted from observable entities and processes that are employed to construct physical objects. It is shown that, for each of the four types of instruction paradigms, there exists an ultra-word-like object such that when an hyper-algorithm is applied to it an ultra-logic-system is hyper-deduced. Another application of an hyper-algorithm yields an hyperfinite instruction paradigm that is hyper-deduced in the required order. It is immediate that duplication of these processes yields a set of hyper-instruction paradigms that satisfies the Patten and Wheeler participator universe requirement. A specific physical data-set is generalized and the set of all ultra-propertons is obtained and its properties examined. This set is shown to be sufficient for universe construction. GGU-model schemes are presented in diagram form. A refinement is introduced that leads, when applied, to the individual development of each universe-wide frozen-frame. An operator is shown to exist, which, via a substratum medium and processes, changes hyper-instruction information into substratum info-fields. From these info-fields all physical and physical-like systems are produced.

**Category:** Mathematical Physics

[124] **viXra:1308.0118 [pdf]**
*replaced on 2014-04-10 07:11:53*

**Authors:** Malcolm Macleod

**Comments:** 5 Pages.

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A principle constraint with constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits which in turn limits the usefulness of Planck theories. By postulating the sqrt of Planck momentum $Q$ as a link between mass and charge, we can formulate the above primary constants as geometrical shapes and then define them in terms of the 4 most accurate constants $c$ (exact), permeability of vacuum $\mu_0$ (exact), Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision) giving us solutions to the Planck units whose precision is limited only by the precision of alpha. A resultant Planck unit theory emerges which suggests that particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. The dimensions of our universe then reduce to the 3 units (dimensions) of motion; Planck momentum, Planck time and velocity c.

**Category:** Mathematical Physics

[123] **viXra:1308.0118 [pdf]**
*replaced on 2014-03-18 11:04:27*

**Authors:** Malcolm Macleod

**Comments:** 5 Pages.

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A principle constraint with constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits which in turn limits the usefulness of Planck theories. By postulating the sqrt of Planck momentum $Q$ as a link between mass and charge, we can formulate the above primary constants as geometrical shapes and then define them in terms of the 4 most accurate constants $c$ (exact), permeability of vacuum $\mu_0$ (exact), Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision) giving us solutions to the Planck units whose precision is limited only by the precision of alpha. A resultant Planck unit theory emerges which suggests that particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. The dimensions of our universe then reduce to the 3 units (dimensions) of motion; Planck momentum, Planck time and velocity c.

**Category:** Mathematical Physics

[122] **viXra:1308.0118 [pdf]**
*replaced on 2014-02-23 04:21:40*

**Authors:** Malcolm Macleod

**Comments:** 5 Pages.

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits. By postulating the sqrt of Planck momentum $Q$ as the link between mass and charge, a 'Planck' ampere $A_Q$ is constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived $\mu_0$ (permeability of vacuum) which in turn gives a formula for Planck length $l_p$ and for a magnetic monopole ($A.l_p$). From the monopole can be formed an electron which is then used to solve the Rydberg constant $R$. Consequently $G$, $h$, $e$, $m_e$... can then be solved in terms of the 4 most accurate constants $c$, $\mu_0$, Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision). Planck temperature $T_P$ and so Boltzmanns constant $k_B$ are functions of the ampere and velocity ($A.c$). The electron formula suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. This wave-particle duality (oscillation) suggests a MUH Mathematical Universe Hypothesis where particles and photons modulate magnetic monopoles. The dimensions of our universe then reduce to the 3 dimensions of motion; Planck momentum, Planck time and velocity c.

**Category:** Mathematical Physics

[121] **viXra:1308.0118 [pdf]**
*replaced on 2014-01-04 23:12:26*

**Authors:** Malcolm Macleod

**Comments:** 5 Pages.

The primary constants; $G$, $c$, $h$, $e$, $\alpha$, $k_B$, $m_e$... range in precision from low $G$ (4-digits) to exact values ($c$, $\mu_0$). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of $G$ and so to 4-digits. By postulating the sqrt of Planck momentum $Q$ as the link between mass and charge, a 'Planck' ampere $A_Q$ is constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived $\mu_0$ (permeability of vacuum) which in turn gives a formula for Planck length $l_p$ and for a magnetic monopole ($A.l_p$). From the monopole can be formed an electron which is then used to solve the Rydberg constant $R$. Consequently $G$, $h$, $e$, $m_e$... can then be solved in terms of the 4 most accurate constants $c$, $\mu_0$, Rydberg constant (12 digit precision) and the fine structure constant alpha $\alpha$ (10 digit precision). Planck temperature $T_P$ and so Boltzmanns constant $k_B$ are functions of the ampere and velocity $A.c$. The electron formula suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) Planck-time-mass point-state oscillation. This wave-particle duality (oscillation) suggests a MUH Mathematical Universe Hypothesis where particles and photons modulate magnetic monopoles. The dimensions of our universe then reduce to the 3 dimensions of motion; sqrt of Planck momentum, Planck time and c.

**Category:** Mathematical Physics

[120] **viXra:1308.0118 [pdf]**
*replaced on 2013-10-09 07:00:22*

**Authors:** Malcolm Macleod

**Comments:** 4 Pages.

The primary constants; G, c, h, e (or mu_0), alpha and m_e range in precision from low G (4-digits) to exact values (c, mu_0). A major problem in constructing a Planck unit theory is that the Planck units are limited to the precision of G. By postulating the sqrt of Planck momentum as a link between mass and charge, a 'Planck' ampere A_Q may be constructed as a geometrical shape; the volume of velocity/mass. From this Planck Ampere can then be derived e and mu_0 (permeability of vacuum). We may then use mu_0 to solve Planck length l_p and this gives a formula for the electron (as a magnetic monopole). G, h, e and m_e can be now be solved using the 4 most accurate constants c, mu_0, Rydberg constant R (12 digit precision) and the fine structure constant alpha alpha (10 digit precision). The electron magnetic monopole suggests a Planck unit theory whereby particles are dimensionless formulas dictating the frequency of Planck events via a periodic (analog) electric wave-state to digital (integer) mass Planck-event (Planck-time) point-state oscillation. This wave-particle duality (oscillation) becomes the basis for a MUH Mathematical Universe Hypothesis. The dimensions of our universe reduce to the 3 units of motion; sqrt of Planck momentum, Planck time and c.

**Category:** Mathematical Physics

[119] **viXra:1308.0091 [pdf]**
*replaced on 2014-03-02 09:35:40*

**Authors:** Peter Waaben

**Comments:** 35 Pages.

An infinitesimal approach

**Category:** Mathematical Physics

[118] **viXra:1308.0080 [pdf]**
*replaced on 2013-09-24 05:12:15*

**Authors:** Branko Zivlak

**Comments:** 6 Pages. 16 formulas, 2 tables

Koide formula has improved on the result 2/3 in the formula (14). The tau lepton mass is also calculated. This is third version of the article.

**Category:** Mathematical Physics

[117] **viXra:1308.0080 [pdf]**
*replaced on 2013-09-22 09:57:33*

**Authors:** Branko Zivlak

**Comments:** 6 Pages. 16 formulas, 2 tables

Abstract. The author corrects the Koide formula to the result 2/3, employing the methods from the articles previously published at viXra.org. The tau lepton mass is also calculated. This is second version of the article.

**Category:** Mathematical Physics

[116] **viXra:1308.0069 [pdf]**
*replaced on 2014-04-19 05:51:03*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 9 Pages.

ABSTRACT: We Study the use of Abel summation applied to the evaluation of infinite
series and infinite (divergent) integrals , we give several examples of how we can
obtain a regularization for the case of divergent sums and integrals.
Keywords: = Abel sum formula,Abel-Plana formula, poles , infinities, renormalization,
regularization, multiple integrals, Casimir effect.

**Category:** Mathematical Physics

[115] **viXra:1306.0236 [pdf]**
*replaced on 2014-03-06 11:06:17*

**Authors:** Leonardo Pedro

**Comments:** 27 Pages. Draft version

We do a study of the real representations of the Poincare group, motivated by the fol-
lowing: i) the classical electromagnetic field —from which the Poincare group was originally
defined— transforms as a real representation of the Poincare group; ii) the localization
of complex unitary representations of the Poincare group is incompatible with causality,
Poincare covariance and energy positivity, while the complex representation corresponding
to the photon is not localizable.
We start by reviewing the map from the complex to the real irreducible representations—
finite-dimensional or unitary—of a Lie group on a Hilbert space.
Then we show that all the finite-dimensional real representations of the identity compo-
nent of the Lorentz group are also representations of the full Lorentz group, in contrast with
many complex representations.
We finally study the unitary irreducible representations of the Poincare group with dis-
crete spin or helicity and show that: for each pair of complex representations with pos-
itive/negative energy, there is one real representation; the localization, compatible with
causality and Poincare covariance, exists for representations with discrete spin or helicity.

**Category:** Mathematical Physics

[114] **viXra:1306.0236 [pdf]**
*replaced on 2013-08-27 17:39:42*

**Authors:** Leonardo Pedro

**Comments:** 22 Pages. Draft version

We study the real representations of the Poincare group and its relation with the complex
representations. The classical electromagnetic field — from which the Poincare group was
originally defined — is a real representation of the Poincare group.
We show that there is a map from the complex to the real irreducible representations of
a Lie group on a Hilbert space — the map is known in the finite-dimensional representations
of a real Lie algebra.
We show that all the finite-dimensional real representations of the restricted Lorentz
group are also representations of the full Lorentz group, in contrast with many complex
representations.
We study the unitary irreducible representations of the Poincare group with discrete spin
and show that for each pair of complex representations with positive/negative energy, there
is one real representation; we show that there are unitary transformations, defining linear
and angular momenta spaces which are common for the real and complex representations.

**Category:** Mathematical Physics

[113] **viXra:1306.0209 [pdf]**
*replaced on 2013-07-20 13:50:22*

**Authors:** Andrew Nassif

**Comments:** 15 Pages. Resubmitted, please see second PDF for better formatting

This is a collection of some of my notes in mathematical physics and Quantum Field Theory. This also includes the P vs. NP computational proof, the Zeta Function Data graphed, Notes on some common topics in Mathematics and Mathematical Physics, and Computational Mathematics as well as Three Dimensional Data Graphing.

**Category:** Mathematical Physics

[112] **viXra:1306.0020 [pdf]**
*replaced on 2013-07-27 17:22:09*

**Authors:** Miguel A. Sanchez-Rey

**Comments:** 16 Pages.

We propose a solution to the Mass Gap and Yang Mills problem establish by the Clay Mathematics Institute.

**Category:** Mathematical Physics

[111] **viXra:1305.0201 [pdf]**
*replaced on 2013-06-20 06:07:51*

**Authors:** Leonardo Pedro

**Comments:** 15 Pages. Draft version

The Majorana spinor is an element of a 4 dimensional real vector space. The
Majorana spinor field is a space-time dependent Majorana spinor, solution of the
free Dirac equation.
We show that the Majorana spinor field with finite mass is a real orthogo-
nal irreducible representation of the Poincare group. The Majorana-Fourier and
Majorana-Hankel transforms of Majorana spinor fields are defined and related to
the linear and angular momentums of a spin one-half representation of the Poincare
group.

**Category:** Mathematical Physics

[110] **viXra:1305.0201 [pdf]**
*replaced on 2013-06-06 08:24:04*

**Authors:** Leonardo Pedro

**Comments:** 15 Pages. Draft version

The Dirac spinor is an element of a 4 dimensional complex vector space, while the
Majorana spinor is an element of a 4 dimensional real vector space. Unlike on the
Dirac spinor, the Lorentz group projective representation on the Majorana spinor is
irreducible, even if parity and time reversal are not included. The spinor fields are space-
time dependent spinors, solutions of the free Dirac equation.
We define the Majorana-Fourier and Majorana-Hankel transforms and relate them
to the linear and angular momenta of a spin one-half representation of the Poincare
group. We show that, even if parity and time reversal are not included, the projective
representation of the Poincare group on the Majorana spinor field is orthogonal and
irreducible, while on the Dirac spinor field it is (anti-)unitary and reducible.

**Category:** Mathematical Physics

[109] **viXra:1305.0171 [pdf]**
*replaced on 2013-07-25 15:35:48*

**Authors:** Jose javier garcia Moreta

**Comments:** 19 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization

**Category:** Mathematical Physics

[108] **viXra:1305.0171 [pdf]**
*replaced on 2013-07-01 15:36:18*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 16 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional

**Category:** Mathematical Physics

[107] **viXra:1305.0171 [pdf]**
*replaced on 2013-06-27 17:07:06*

**Authors:** Jose Javier garcia Moreta

**Comments:** 15 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization

**Category:** Mathematical Physics

[106] **viXra:1305.0085 [pdf]**
*replaced on 2013-08-09 16:17:16*

**Authors:** Nathan O. Schmidt

**Comments:** 30 pages, 2 figures, published in the Hadronic Journal

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.

**Category:** Mathematical Physics

[105] **viXra:1305.0085 [pdf]**
*replaced on 2013-07-05 21:49:21*

**Authors:** Nathan O. Schmidt

**Comments:** 30 pages, 2 figures, published in the Hadronic Journal

In this work, we forge a powerful, easy-to-visualize, flexible, consistent, and disciplined abstract vector framework for particle and astro physics that is compliant with the holographic principle. We demonstrate that the structural properties of the complex number and the sphere enable us to introduce and define the triplex number---an influential information structure that is similar to the 3D hyper-complex number by D. White and P. Nylander---which identifies a 3D analogue of (2D) complex space. Consequently, we engage the complex and triplex numbers as abstract vectors to systematically encode the state space of the Riemannian dual 3D and 4D space-time topologies, where space and time are dual and interconnected; we use the triplex numbers (with triplex multiplication) to extend 1D and 2D algebraic systems to 3D and 4D configurations. In doing so, we equip space-time with order parameter fields for topological deformations. Finally, to exemplify our motivation, we provide three example applications for this framework.

**Category:** Mathematical Physics

[104] **viXra:1304.0106 [pdf]**
*replaced on 2013-05-18 22:57:55*

**Authors:** Vyacheslav Telnin

**Comments:** 7 Pages.

This paper deals with the generalizations of the First Noether theorem. It takes into
account not only the first derivatives of the fields by the coordinates in Lagrangian, but
also the second. And this theorem is generalized on the curved spaces. And also it's
generalized on asymmetric metric tensors.

**Category:** Mathematical Physics

[103] **viXra:1304.0013 [pdf]**
*replaced on 2013-08-26 05:01:28*

**Authors:** Jose Javier garcia Moreta

**Comments:** 18 Pages.

ABSTRACT: In this paper we study the methods of Borel resummation applied
to the solution of integral equation with symmetric Kernels K(xs) and to the study of the
Riesz criterion , which is important to the Riemann Hypothesis
•Keywords: Integral equation, Borel resummation, divergent series

**Category:** Mathematical Physics

[102] **viXra:1304.0013 [pdf]**
*replaced on 2013-08-16 06:23:06*

**Authors:** Jose Javier garcia Moreta

**Comments:** corrected several grammar misakes added more pages

ABSTRACT: In this paper we study the methods of Borel resummation applied
to the solution of integral equation with symmetric Kernels K(xs) and to the study of the
Riesz criterion , which is important to the Riemann Hypothesis

**Category:** Mathematical Physics

[101] **viXra:1304.0013 [pdf]**
*replaced on 2013-07-12 07:48:22*

**Authors:** Jose javier garcia Moreta

**Comments:** 12 Pages.

ABSTRACT: In this paper we study the methods of Borel resummation applied
to the solution of integral equation with symmetric Kernels K(xs) and to the study of the
Riesz criterion , which is important to the Riemann Hypothesis

**Category:** Mathematical Physics

[100] **viXra:1304.0010 [pdf]**
*replaced on 2013-06-28 15:16:39*

**Authors:** Dan Visser

**Comments:** 12 Pages. Version 2 on June 28 2013 (textual and calculation-corrections)

The Double Torus hypothesis stands for a new architecture for the Universe. Based on practical evidence, another dark energy drives the dynamics making the Big Bang an illusion. There has not been a Big Bang! New dark energy applies two extra time-clocks from below the Planck-time to dark matter. The implication is: The universe exists of a Double Torus of the dark energy-time enclosing and intertwining an inner dark matter torus. This might sound controversial, but a new ‘dark energy-force formula’ and related calculations, described within the Double Torus framework in several ‘papers’, enables a match with real observed phenomena, such as: 1) A smallest Newton-acceleration, a dark matter-acceleration in galaxies, 2) an anomalous deceleration of the Pioneer 1 and 2 satellites, 3) a dark flow of spatial dark matter, 4) a solution eliminating the discrepancy of vacuum-energy-density (between General Relativity and Quantum-Mechanics calculations), 5) an α-dipole that indicates a torus-shape for the universe, 6) four times shifted ‘hot- and cold spots’ in the CMB, 7) an explanation for why 4,9% matter is visible, 26,8% is dark matter and 67,3% is dark energy and 8) at last why for ½ the squared-Planck-length gravity turns into anti-gravity. All the issues for evidence are described in my former ‘papers’ (see references), whereof the last two ones are in concept and will be published soon. However, particularly this paper relates to the combination of Newton quantum-gravity-force and dark matter-force, both implemented in one (new) formula. The dark matter force could be gravitational (+) and (-) , which means an anti-gravitational property of dark matter is highlighted in this paper. In this respect the measured laboratory acceleration-limit for Newton-gravity, 5 x 10^-14 m/s^2, theoretically is set to a lower value of 2.8659 x 10^-14 m/s^2. That is remarkable, because no other formula in science is at hand for that. In general the dynamics for the Double Torus hypothesis is developed by DAN Visser, Almere, the Netherlands. He is an independent cosmologist and painting-artist. His conclusion is: The universe did not start with a Big Bang, but is a rotational cyclic-curved Double Torus, which recalculates reality eternally and independent on the scale one imagines the walls of the universe.

**Category:** Mathematical Physics

[99] **viXra:1303.0090 [pdf]**
*replaced on 2013-12-14 15:25:42*

**Authors:** Florentino Muñiz Ania

**Comments:** 2 pages, 3 figures

This article shows how the gravitational force is conservative only in ideal models of small
size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems.
Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general,
no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos.

**Category:** Mathematical Physics

[98] **viXra:1303.0090 [pdf]**
*replaced on 2013-03-27 10:34:03*

**Authors:** Florentino Muñiz Ania

**Comments:** 2 Pages. Sólo hablo español.

This article shows how the gravitational force is conservative only in ideal models of small
size. It is shown as strictly mathematical generally is not conservative. From it you can get energy by asymmetric systems.
Spanish: En este artículo se muestra como la fuerza gravitatoria sólo es conservativa en modelos ideales de pequeño tamaño. Se demuestra con rigor matemático como, en general, no es conservativa. De ella se puede obtener energía mediante sistemas asimétricos.
vixra.org@gmail.com

**Category:** Mathematical Physics

[97] **viXra:1302.0095 [pdf]**
*replaced on 2013-07-09 00:23:49*

**Authors:** Hosein Nasrolahpour

**Comments:** 5 Pages.

The fractional variational principle represents an important part of fractional calculus and has
found many applications. There are several versions of fractional variational principles and so
different kinds of fractional Euler-Lagrange equations. In this paper, we propose the fractional
sine-Gordon Lagrangian density. Then using the fractional Euler-Lagrange equations we obtain
fractional sine-Gordon equation.

**Category:** Mathematical Physics

[96] **viXra:1301.0078 [pdf]**
*replaced on 2013-02-08 08:52:48*

**Authors:** Jose Javier Garcia

**Comments:** 11 Pages.

We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential.

**Category:** Mathematical Physics

[95] **viXra:1301.0078 [pdf]**
*replaced on 2013-01-21 13:14:38*

**Authors:** Jose Javier Garcia

**Comments:** 11 Pages.

We study the relation between the Guzwiller Trace for a dynamical system and the Riemann-Weil trace formula for the Riemann zeros, using the Bohr-Sommerfeld quantization condition and the fractional calculus we obtain a method to define implicitly a potential , we apply this method to define a Hamiltonian whose energies are the square of the Riemann zeros (imaginary part) , also we show that for big ‘x’ the potential is very close to an exponential function. In this paper and for simplicity we use units so • Keywords: = Riemann Hypothesis, WKB semiclassical approximation, Gutzwiller trace formula, Bohr-Sommerfeld quantization,exponential potential.

**Category:** Mathematical Physics

[94] **viXra:1301.0076 [pdf]**
*replaced on 2014-04-08 12:53:00*

**Authors:** Sergey A. Kamenshchikov

**Comments:** 8 Pages.

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.

**Category:** Mathematical Physics

[93] **viXra:1301.0076 [pdf]**
*replaced on 2014-04-08 00:17:28*

**Authors:** Sergey A. Kamenshchikov

**Comments:** 8 Pages.

The goal of this investigation was to derive strictly new properties of chaotic systems and their mutual relations. The generalized Fokker-Planck equation with a non stationary diffusion has been derived and used for chaos analysis. An anomalous transport turned out to be natural property of this equation. A nonlinear dispersion of the considered motion allowed to find a principal consequence: a chaotic system with uniform dynamic properties tends to instable clustering. Small fluctuations of particles density increase by time and form attractors and stochastic islands even if the initial transport properties have uniform distribution. It was shown that an instability of phase trajectories leads to the nonlinear dispersion law and consequently to a space instability. A fixed boundary system was considered, using a standard Fokker-Planck equation. We have derived that such a type of dynamic systems has a discrete diffusive and energy spectra. It was shown that phase space diffusion is the only parameter that defines a dynamic accuracy in this case. The uncertainty relations have been obtained for conjugate phase space variables with account of transport properties. Given results can be used in the area of chaotic systems modelling and turbulence investigation.

**Category:** Mathematical Physics

[92] **viXra:1301.0076 [pdf]**
*replaced on 2013-03-13 07:10:48*

**Authors:** Sergey Kamenshchikov

**Comments:** 12 Pages. Author is looking for postdoc position. kamphys@gmail.com

The purpose of this work was to introduce strict, comprehensive definition of perfect chaos, to find out its basic properties in terms of phase transitions and give connections for uncertainties, lying in base of perfect chaos concept. Concept of perfect chaos as undetermined description was introduced basing on two formalized necessary and sufficient conditions: finite phase space resolution and instability of phase space trajectories. Properties of Kolmogorov system, including phase mixing, turned out to be consequences of chaotic state but not its comprehensive and sufficient conditions.Description relativity was defined as mandatory property of perfect chaos. The same areas of phase space may show regular or chaotic properties depending on space - time description accuracy. Herewith evolution of physical system in given generalized phase space can be represented by consequence of regular states and intermediate transitions. For chaotic state with uniform diffusion it was found out that nonlinear dispersion law is mandatory property.One in its turn necessarily leads to space - time instability of probability density and appearance of probability cavities in phase space - phase space attractors where particles density grows up. Case of chaotic state with fixed boundary and diffusion was considered. It turned out that Fourier decomposition allows to derive relations between coordinate - momentum and time - energy definition uncertainties. It was shown that chaos diffusion factor is the only parameter, limiting product of corresponding uncertainties.

**Category:** Mathematical Physics

[91] **viXra:1212.0081 [pdf]**
*replaced on 2013-01-06 01:38:58*

**Authors:** Hosein Nasrolahpour

**Comments:** 3 Pages. Another short report on " Fractional Classical Mechanics" :Prespacetime Journal| November 2012 | Volume 3| Issue 13 | pp. 1247-1250

In this paper we discuss some important consequences of application of fractional operators in
physics. Also we present a unified integro-differential equation for relaxation and oscillation. We
focus on time fractional formalism whose derivative is in Caputo sense.

**Category:** Mathematical Physics

[90] **viXra:1211.0143 [pdf]**
*replaced on 2014-04-19 05:52:35*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 10 Pages.

ABSTRACT: We study a given exponential potential
aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method
to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue
staircase includes the oscillatory and smooth part of the Number of Riemann zeros.
In this paper and for simplicity we use units so 2m1
Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential

**Category:** Mathematical Physics

[89] **viXra:1211.0143 [pdf]**
*replaced on 2014-03-14 14:23:41*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 10 Pages.

ABSTRACT: We study a given exponential potential on the Real half-line which is possible related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue staircase includes the oscillatory and smooth part of the Number of Riemann zeros.
In this paper and for simplicity we use units so
•Keywords: = Riemann Hypothesis, WKB semiclassical approximation, exponential potential.

**Category:** Mathematical Physics

[88] **viXra:1211.0143 [pdf]**
*replaced on 2013-01-02 14:31:57*

**Authors:** Jose Javier Garcia

**Comments:** 8 Pages.

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method
to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue

**Category:** Mathematical Physics

[87] **viXra:1211.0143 [pdf]**
*replaced on 2012-12-13 05:41:21*

**Authors:** Jose Javier Garcia

**Comments:** 8 Pages.

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method
to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue
staircase includes the oscillatory and smooth part of the Number of Riemann zeros.
In this paper and for simplicity we use units so 2m =1= h
· Keywords: = Riemann

**Category:** Mathematical Physics

[86] **viXra:1211.0143 [pdf]**
*replaced on 2012-11-29 04:29:08*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 7 Pages.

ABSTRACT: We study a given exponential potential aebx on the Real half-line which is possible
related to the imaginary part of the Riemann zeros. We extend alsostudy also our WKB method
to recover the potential from the Eigenvalue Staircase for the Riemann zeros, this eigenvalue
staircase includes the oscillatory and smooth part of the Number of Riemann

**Category:** Mathematical Physics

[85] **viXra:1211.0051 [pdf]**
*replaced on 2013-04-02 13:59:43*

**Authors:** Hosein Nasrolahpour

**Comments:** 7 Pages. A few formulas and references added.

We investigate the time evolution of the fractional electromagnetic waves by using the time
fractional Maxwell's equations. We show that electromagnetic plane wave has amplitude which
exhibits an algebraic decay, at asymptotically long times.

**Category:** Mathematical Physics

[84] **viXra:1210.0123 [pdf]**
*replaced on 2012-11-19 15:12:36*

**Authors:** John A. Gowan

**Comments:** 6 Pages.

In the mathematical terms of Evariste Galois' "Group Theory", the "Tetrahedron Model" is a description of the symmetry group of light, including its destruction by asymmetric weak force decays (producing our matter-only Cosmos), and its on-going restoration in obedience to Noether's Theorem of symmetry conservation (as in the conversion of bound to free energy in stars).
The usual symmetry group identified with light is that of local phase transformations, and it is designated as either SO(2) or U(1). However, I am suggesting here that light contains a very much larger (and more interesting) symmetry group associated with its transformation into particle-antiparticle pairs (and back again into light). I don't know what the formal designation of this group might be.
For an expert's explanation of the formal aspects of symmetry and group theory, See: Keith Devlin The Language of Mathematics Chap. 5 "The Mathematics of Beauty", 1998 W. H. Freeman & Co. (Holt Paperbacks); see also: Ian Stewart Why Beauty is Truth Chapt. 13 "The Five Dimensional Man", Basic Books 2007.

**Category:** Mathematical Physics

[83] **viXra:1210.0123 [pdf]**
*replaced on 2012-11-10 12:47:27*

**Authors:** John A. Gowan

**Comments:** 5 Pages.

A symmetry group consists (for one example) of a collection of figures that can be transformed into one another without changing the original. The symmetry group of an equilateral triangle (say) consists of all the triangles that can be created from an original by means of rotation, translation, reflection, etc. - provided the transformed articles are indistinguishable from the original. How do we apply this notion to the case of light? In what sense is there a symmetry group associated with (consisting of) transformations of light (free electromagnetic radiation)?
Beyond the simple phase transformations of the electromagnetic field, the examples of interest here are the particle-antiparticle pairs of the Dirac/Heisenberg "vacuum" of spacetime. These particle-antiparticle pairs are constantly produced from borrowed energy and instantaneously annihilate each other in an endless cycle of creation and destruction alternating between light and virtual particles, a cycle which has been ongoing throughout spacetime since its beginning in the "Big Bang". Since they are "virtual" rather than "real" particles we do not notice them even though they are everywhere around us. Essentially, we do not notice them because their symmetry is so complete. We only notice the asymmetries which surround (and comprise) us.

**Category:** Mathematical Physics

[82] **viXra:1210.0123 [pdf]**
*replaced on 2012-11-01 15:42:48*

**Authors:** John A. Gowan

**Comments:** 5 Pages. A table is added to the original paper

A symmetry group consists (for one example) of a collection of figures that can be transformed into one another without changing the original. The symmetry group of an equilateral triangle (say) consists of all the triangles that can be created from an original by means of rotation, translation, reflection, etc. - provided the transformed articles are indistinguishable from the original. How do we apply this notion to the case of light? In what sense is there a symmetry group associated with (consisting of) transformations of light (free electromagnetic radiation)?
Beyond the simple phase transformations of the electromagnetic field, the examples of interest here are the particle-antiparticle pairs of the Dirac/Heisenberg "vacuum" of spacetime. These particle-antiparticle pairs are constantly produced from borrowed energy and instantaneously annihilate each other in an endless cycle of creation and destruction alternating between light and virtual particles, a cycle which has been ongoing throughout spacetime since its beginning in the "Big Bang". Since they are "virtual" rather than "real" particles we do not notice them even though they are everywhere around us. Essentially, we do not notice them because their symmetry is so complete. We only notice the asymmetries which surround (and comprise) us.

**Category:** Mathematical Physics

[81] **viXra:1210.0114 [pdf]**
*replaced on 2012-11-05 13:03:49*

**Authors:** Jose M. Hernandez

**Comments:** 4 Pages.

is fine

**Category:** Mathematical Physics

[80] **viXra:1210.0114 [pdf]**
*replaced on 2012-10-24 15:21:37*

**Authors:** Jose M Hernandez

**Comments:** 4 Pages. view

is fine

**Category:** Mathematical Physics

[79] **viXra:1207.0089 [pdf]**
*replaced on 2012-09-07 09:16:02*

**Authors:** Laszlo B. Kish, Claes-Göran Granqvist

**Comments:** 17 Pages. Accepted for publication in PLOS ONE (September 6, 2012)

We introduce a purely electrical version of Maxwell’s demon which does not involve mechanically moving parts such as trapdoors, etc. It consists of a capacitor, resistors, amplifiers, logic circuitry and electronically controlled switches and uses thermal noise in resistors (Johnson noise) to pump heat. The only types of energy of importance in this demon are electrical energy and heat. We also demonstrate an entirely electrical version of Szilard’s engine, i.e., an information-controlled device that can produce work by employing thermal fluctuations. The only moving part is a piston that executes work, and the engine has purely electronic controls and it is free of the major weakness of the original Szilard engine in not requiring removal and repositioning the piston at the end of the cycle. For both devices, the energy dissipation in the memory and other binary informatics components are insignificant compared to the exponentially large energy dissipation in the analog part responsible for creating new information by measurement and decision. This result contradicts the view that the energy dissipation in the memory during erasure is the most essential dissipation process in a demon. Nevertheless the dissipation in the memory and information processing parts is sufficient to secure the Second Law of Thermodynamics.

**Category:** Mathematical Physics

[78] **viXra:1206.0069 [pdf]**
*replaced on 2012-09-26 14:59:59*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 13 Pages.

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function. In this paper and for simplicity we use units so
• Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula ,Bolte’s law, Quantum chaos.

**Category:** Mathematical Physics

[77] **viXra:1206.0069 [pdf]**
*replaced on 2012-08-26 07:01:41*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 15 Pages.

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function. In this paper and for simplicity we use units so
• Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula ,Bolte’s law, Quantum chaos.

**Category:** Mathematical Physics

[76] **viXra:1206.0069 [pdf]**
*replaced on 2012-07-06 06:09:46*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 14 Pages. upadted with more equations, corrected several errors

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function • Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical Approximation , Trace formula ,Bolte’s law, Quantum chaos.

**Category:** Mathematical Physics

[75] **viXra:1206.0069 [pdf]**
*replaced on 2012-06-25 04:35:14*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 12 Pages.

• ABSTRACT: We give and interpretation of the Riemann Xi-function as the quotient of two functional determinants of an Hermitian Hamiltonian . To get the potential of this Hamiltonian we use the WKB method to approximate and evaluate the spectral Theta function over the Riemann zeros on the critical strip . Using the WKB method we manage to get the potential inside the Hamiltonian , also we evaluate the functional determinant by means of Zeta regularization, we discuss the similarity of our method to the method applied to get the Zeros of the Selberg Zeta function
• Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula ,Bolte’s law, Quantum chaos.

**Category:** Mathematical Physics

[74] **viXra:1206.0064 [pdf]**
*replaced on 2013-01-05 04:47:27*

**Authors:** Hosein Nasrolahpour

**Comments:** 10 Pages.

In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can provide a deeper understanding of the physical interpretations of fractional derivative.

**Category:** Mathematical Physics

[73] **viXra:1206.0049 [pdf]**
*replaced on 2012-07-29 15:28:19*

**Authors:** Thomas J. Buckholtz

**Comments:** 15 Pages.

We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Some ratios of numbers of instances of various types of particles are 1:6:24:48. Potentially, the actual ratios of densities of baryonic matter, dark matter, dark energy are 1:5:18 and do not depend on time, even though interpretations of data provide ratios that vary with the age of the universe. Potentially there is another type of stuff. Here, 5=6-1, 18=24-6, and there could be 24=48-24 units of the other type of stuff.

**Category:** Mathematical Physics

[72] **viXra:1206.0049 [pdf]**
*replaced on 2012-07-23 15:55:48*

**Authors:** Thomas J. Buckholtz

**Comments:** 15 Pages.

We develop theory leading to an ability to catalog types of elementary particles. The resulting catalog provides for known interaction-mediating bosons, non-traditional interaction-carrying bosons, and fermions. Ratios of theoretical numbers of analogs of various types of particles may be consistent with observed ratios of densities for baryonic matter, dark matter, and dark energy.

**Category:** Mathematical Physics

[71] **viXra:1204.0043 [pdf]**
*replaced on 2012-05-20 06:08:09*

**Authors:** Dan Visser

**Comments:** 10 Pages.

Neutrinos-faster-than-light? The science-battle is not yet over! ‘Yes’, said the OPERA-team in September 22 2011. ‘No’, said the ICARUS-team in February 23 2012. But this paper carries on that it is undoubtedly correct that neutrinos can go faster-than-light. Neutrinos can only do that in neutrino-pairs: I call these pairs Duonistic Neutrinos! This paper presents the set of equations to prove that. The smallest gravity-acceleration g’ appears to be prior to the trajectory of single packaged neutrinos. OPERA and ICARUS might be right both in the end.

**Category:** Mathematical Physics

[70] **viXra:1203.0067 [pdf]**
*replaced on 2013-03-24 16:48:31*

**Authors:** Robert Watson

**Comments:** 34 Pages. ...looking better now...

Kaluza's 1921 theory of gravity and electromagnetism using a fifth
wrapped-up spatial dimension is at the root of many modern attempts to
develop new physical theories. Lacking non-null electromagnetic fields however the
theory is incomplete. Variants of the theory are explored to find ways to introduce non-null solutions
by making the fifth dimension more physical, using alternative, weaker cylinder conditions.
The Lorentz force law is investigated starting
with a non-Maxwellian definition of charge, this is assumed to be related to Maxwellian charge by ansatz.
Order of magnitude methods are used.
Kaluza theory remains inadequate to support electromagnetism in full,
non-null solutions are not readily shown to be admitted. An argument is made in favour of torsion resolving this issue.
Postulates are derived from the argument for a variant theory.
The charge ansatz is shown to follow from the postulates.
It is concluded that Kaluza's 5D space and torsion need to go together in a Kaluza-Cartan theory. Tentatively, generalized Bel super-energy is hypothesized to be
a conserved quantity.

**Category:** Mathematical Physics

[69] **viXra:1201.0117 [pdf]**
*replaced on 2013-06-29 15:21:39*

**Authors:** Dan Visser

**Comments:** 10 Pages. This version-2 of June 29 2013 comprehends important notes: My formulas used in the appendix (letter to the Nobel Committee) are much more analyzed afterwards in following ‘papers’. So this moment, June 29 2013, I decided to keep this paper active.

This paper describes an interim stage in the Double Torus hypothesis’ development. I also implemented a message of “Nobel Nominations in a New World” to the Nobel Committee. These seemingly different looking subjects are importantly connected in a plead to change the way Nobel-nominations are performed in a changing world with internet and alternative archives, such as viXra. The point is here, that institutional established physics and cosmology are blocking new ideas from the public domain. Therefore an appendix has been added to this paper to summarize in a nutshell, relativity, space-expansion, accelerated space-expansion and the one time-direction in the Big Bang Cosmology, in order to explain better what new dark energy is in the Double Torus. That message is meant for the Nobel Committee. Furthermore three-why’s are answered: Why are two extra time-directions needed in a new cosmology? Why is the introduction of dark mass, squared? Why would there be a Double Torus for New Cosmology? Also the basic-formulas are summarized, referring to my papers, such as the dark energy force formula from my thought-experiment, followed by its transformed-version: the force smaller than the smallest gravity. In the end New Dark Energy is formulated as a product of new dark mass (squared) and two extra time-directions from below the Planck scale. This marks that New Dark Energy could recalculate the established dual unitary-entangled quantum-spaces faster backwards in time than time goes forward in the Big Bang Cosmology! This affects the established quantum dynamics and classical reality towards the past and future differently than Einstein’s General Relativity is prescribing. The letter to the Nobel Committee is send by me, because no other institutions is doing that for me.

**Category:** Mathematical Physics

[68] **viXra:1112.0094 [pdf]**
*replaced on 2012-09-07 10:45:39*

**Authors:** DT Froedge

**Comments:** 15 Pages. This should be the final. Accuracies calculated in parts per billion

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, yielding specific values for some well studied particles. The additional nuclear modes postulated, are similar to the Schrodinger modes in the atom, and the mass ratios calculated for these particles have been calculated within the experimental values, with accuracies up to 2.4 parts per billion. The examined particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0.

**Category:** Mathematical Physics

[67] **viXra:1112.0094 [pdf]**
*replaced on 2012-08-18 08:31:46*

**Authors:** DT Froedge

**Comments:** 14 Pages. Finally, very precise values.

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values. Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0

**Category:** Mathematical Physics

[66] **viXra:1112.0094 [pdf]**
*replaced on 2012-08-14 21:31:58*

**Authors:** DT Froedge

**Comments:** 13 Pages. This worked out

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values. Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0

**Category:** Mathematical Physics

[65] **viXra:1112.0094 [pdf]**
*replaced on 2012-08-13 21:58:31*

**Authors:** DT Froedge

**Comments:** 14 Pages. finally figured it out,

Based on the developments in a previous paper, this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles have been calculated within the experimental values.Those particles are the Proton, Neutron, Muon, Tauon, and Pion+/-/0.

**Category:** Mathematical Physics

[64] **viXra:1112.0094 [pdf]**
*replaced on 2012-07-22 13:23:18*

**Authors:** DT Froedge

**Comments:** 10 Pages. Major improvement, ongoing project.

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and the mass ratios calculated for elementary particles are very close the observed mass ratios. Integral amplitudes for the Pauli and quark matrix are shown to produce values that are far more accurate than those that could be produced by random coincidence.

**Category:** Mathematical Physics

[63] **viXra:1112.0094 [pdf]**
*replaced on 2012-07-07 14:28:58*

**Authors:** DT Froedge

**Comments:** 13 Pages. A little progress.

Based on the developments in a previous paper, this paper presents straightforward explanation
of particle mass ratios, and the specific values for some well known particles. The additional nuclear
modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative,
the mass ratios calculated for elementary particles are very close the observed mass ratios.

**Category:** Mathematical Physics

[62] **viXra:1112.0094 [pdf]**
*replaced on 2012-06-07 14:41:38*

**Authors:** DT Froedge

**Comments:** 14 Pages. Minor Corrections

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.

**Category:** Mathematical Physics

[61] **viXra:1112.0094 [pdf]**
*replaced on 2012-03-11 12:59:44*

**Authors:** DT Froedge

**Comments:** 12 Pages. This is the 6Th and final revision (v3-11-12),

Based on the developments in a previous paper [1], this paper presents straightforward explanation of particle mass ratios, and the specific values for some well known particles. The additional nuclear modes postulated, are similar to the Schrödinger modes in the atom, and, though speculative, the mass ratios calculated for elementary particles are very close the observed mass ratios.

**Category:** Mathematical Physics

[60] **viXra:1111.0106 [pdf]**
*replaced on 2013-11-10 15:33:06*

**Authors:** Dan Visser

**Comments:** 7 Pages.

In this version 3 the formulations are given for the existence of a force smaller than the smallest gravity. This is a new dark energy force, which affects neutrinos differently than is assumed according to current physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. A deeper analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on these issues are far from criticism. My set of equations mentioned in my paper “A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos” and “Duonistic Neutrinos Violate Relativity” reveal such a criticism. However, until now my formulations withstand a hurricane, even after a Director of the OPERA-project had to resign. My set of equations theoretically proves the neutrino-faster-than-light experiments had to be investigated to the bottom.

**Category:** Mathematical Physics

[59] **viXra:1111.0106 [pdf]**
*replaced on 2012-05-16 14:36:33*

**Authors:** Dan Visser

**Comments:** 7 Pages.

In this version2 the formulations are given for the existence of a force smaller than the smallest gravity. This is a new dark energy force, which affects neutrinos differently than is assumed according to current physics. The formulations also imply a different look on the Higgs-mass and dark matter-mass. A deeper analysis became important, because a new cosmological hypothesis is involved. The CERN-experiments on these issues are far from criticism. My set of equations mentioned in my paper “A New Dark Energy Force Theoretically Calculates Faster-than-light-neutrinos” and “Duonistic Neutrinos Violate Relativity”, reveal such a criticism. However, until now my formulations withstand a hurricane, even after a Director of the OPERA-project had to resign. My set of equations theoretically proves the neutrino-faster-than-light experiments had to be investigated to the bottom.

**Category:** Mathematical Physics

[58] **viXra:1111.0091 [pdf]**
*replaced on 2012-01-30 08:18:27*

**Authors:** Matti Pitkänen

**Comments:** 24 Pages.

The arguments of this article support the view that in TGD Universe number theoretic and geometric Langlands conjectures could be understood very naturally. The basic notions are following.

- Zero energy ontology (ZEO) and the related notion of causal diamond CD (CD is short hand for the cartesian product of causal diamond of M
^{4}and of CP_{2}). ZEO leads to the notion of partonic 2-surfaces at the light-like boundaries of CD and to the notion of string world sheet. These notions are central in the recent view about TGD. One can assign to the partonic 2-surfaces a conformal moduli space having as additional coordinates the positions of braid strand ends (punctures). By electric-magnetic duality this moduli space must correspond closely to the moduli space of string world sheets. - Electric-magnetic duality realized in terms of string world sheets and partonic 2-surfaces. The group G and its Langlands dual
^{L}G would correspond to the time-like and space-like braidings. Duality predicts that the moduli space of string world sheets is very closely related to that for the partonic 2-surfaces. The strong form of 4-D general coordinate invariance implying electric-magnetic duality and S-duality as well as strong form of holography indeed predicts that the collection of string world sheets is fixed once the collection of partonic 2-surfaces at light-like boundaries of CD and its sub-CDs is known. - The proposal is that finite measurement resolution is realized in terms of inclusions of hyperfinite factors of type II
_{1}at quantum level and represented in terms of confining effective gauge group. This effective gauge group could be some associate of G: gauge group, Kac-Moody group or its quantum counterpart, or so called twisted quantum Yangian strongly suggested by twistor considerations. At space-time level the finite measurement resolution would be represented in terms of braids at space-time level which come in two varieties correspond to braids assignable to space-like surfaces at the two light-like boundaries of CD and with light-like 3-surfaces at which the signature of the induced metric changes and which are identified as orbits of partonic 2-surfaces connecting the future and past boundaries of CDs.There are several steps leading from G to its twisted quantum Yangian. The first step replaces point like particles with partonic 2-surfaces: this brings in Kac-Moody character. The second step brings in finite measurement resolution meaning that Kac-Moody type algebra is replaced with its quantum version. The third step brings in zero energy ontology: one cannot treat single partonic surface or string world sheet as independent unit: always the collection of partonic 2-surfaces and corresponding string worlds sheets defines the geometric structure so that multilocality and therefore quantum Yangian algebra with multilocal generators is unavoidable.

In finite measurement resolution geometric Langlands duality and number theoretic Langlands duality are very closely related since partonic 2-surface is effectively replaced with the punctures representing the ends of braid strands and the orbit of this set under a discrete subgroup of G defines effectively a collection of "rational" 2-surfaces. The number of the "rational" surfaces in geometric Langlands conjecture replaces the number of rational points of partonic 2-surface in its number theoretic variant. The ability to compute both these numbers is very relevant for quantum TGD.

- The natural identification of the associate of G is as quantum Yangian of Kac-Moody type group associated with Minkowskian open string model assignable to string world sheet representing a string moving in the moduli space of partonic 2-surface. The dual group corresponds to Euclidian string model with partonic 2-surface representing string orbit in the moduli space of the string world sheets. The Kac-Moody algebra assigned with simply laced G is obtained using the standard tachyonic free field representation obtained as ordered exponentials of Cartan algebra generators identified as transversal parts of M
^{4}coordinates for the braid strands. The importance of the free field representation generalizing to the case of non-simply laced groups in the realization of finite measurement resolution in terms of Kac-Moody algebra cannot be over-emphasized. - Langlands duality involves besides harmonic analysis side also the number theoretic side. Galois groups (collections of them) defined by infinite primes and integers having representation as symplectic flows defining braidings. I have earlier proposed that the hierarchy of these Galois groups define what might be regarded as a non-commutative homology and cohomology. Also G has this kind of representation which explains why the representations of these two kinds of groups are so intimately related. This relationship could be seen as a generalization of the MacKay correspondence between finite subgroups of SU(2) and simply laced Lie groups.
- Symplectic group of the light-cone boundary acting as isometries of the WCW geometry kenociteallb/compl1 allowing to represent projectively both Galois groups and symmetry groups as symplectic flows so that the non-commutative cohomology would have braided representation. This leads to braided counterparts for both Galois group and effective symmetry group.
- The moduli space for Higgs bundle playing central role in the approach of Witten and Kapustin to geometric Landlands program is in TGD framework replaced with the conformal moduli space for partonic 2-surfaces. It is not however possible to speak about Higgs field although moduli defined the analog of Higgs vacuum expectation value. Note that in TGD Universe the most natural assumption is that all Higgs like states are "eaten" by gauge bosons so that also photon and gluons become massive. This mechanism would be very general and mean that massless representations of Poincare group organize to massive ones via the formation of bound states. It might be however possible to see the contribution of p-adic thermodynamics depending on genus as analogous to Higgs contribution since the conformal moduli are analogous to vacuum expectation of Higgs field.

[57] **viXra:1111.0090 [pdf]**
*replaced on 2012-01-30 08:22:30*

**Authors:** Matti Pitkänen

**Comments:** 16 Pages.

Infinite primes is a purely TGD inspired notion. The notion of infinity is number theoretical and infinite primes have well defined divisibility properties. One can partially order them by the real norm. p-Adic norms of infinite primes are well defined and finite. The construction of infinite primes is a hierarchical procedure structurally equivalent to a repeated second quantization of a supersymmetric arithmetic quantum field theory. At the lowest level bosons and fermions are labelled by ordinary primes. At the next level one obtains free Fock states plus states having interpretation as bound many particle states. The many particle states of a given level become the single particle states of the next level and one can repeat the construction ad infinitum. The analogy with quantum theory is intriguing and I have proposed that the quantum states in TGD Universe correspond to octonionic generalizations of infinite primes. It is interesting to compare infinite primes (and integers) to the Cantorian view about infinite ordinals and cardinals. The basic problems of Cantor's approach which relate to the axiom of choice, continuum hypothesis, and Russell's antinomy: all these problems relate to the definition of ordinals as sets. In TGD framework infinite primes, integers, and rationals are defined purely algebraically so that these problems are avoided. It is not surprising that these approaches are not equivalent. For instance, sum and product for Cantorian ordinals are not commutative unlike for infinite integers defined in terms of infinite primes.

Set theory defines the foundations of modern mathematics. Set theory relies strongly on classical physics, and the obvious question is whether one should reconsider the foundations of mathematics in light of quantum physics. Is set theory really the correct approach to axiomatization?

- Quantum view about consciousness and cognition leads to a proposal that p-adic physics serves as a correlate for cognition. Together with the notion of infinite primes this suggests that number theory should play a key role in the axiomatics.
- Algebraic geometry allows algebraization of the set theory and this kind of approach suggests itself strongly in physics inspired approach to the foundations of mathematics. This means powerful limitations on the notion of set.
- Finite measurement resolution and finite resolution of cognition could have implications also for the foundations of mathematics and relate directly to the fact that all numerical approaches reduce to an approximation using rationals with a cutoff on the number of binary digits.
- The TGD inspired vision about consciousness implies evolution by quantum jumps meaning that also evolution of mathematics so that no fixed system of axioms can ever catch all the mathematical truths for the simple reason that mathematicians themselves evolve with mathematics.

[56] **viXra:1111.0089 [pdf]**
*replaced on 2012-01-30 08:24:00*

**Authors:** Matti Pitkänen

**Comments:** 80 Pages.

In this article the goal is to find whether the general mathematical structures associated with twistor approach, superstring models and M-theory could have a generalization or a modification in TGD framework. The contents of the chapter is an outcome of a rather spontaneous process, and represents rather unexpected new insights about TGD resulting as outcome of the comparisons.

*1. Infinite primes, Galois groups, algebraic geometry, and TGD*

In algebraic geometry the notion of variety defined by algebraic equation is very general: all number fields are allowed. One of the challenges is to define the counterparts of homology and cohomology groups for them. The notion of cohomology giving rise also to homology if Poincare duality holds true is central. The number of various cohomology theories has inflated and one of the basic challenges to find a sufficiently general approach allowing to interpret various cohomology theories as variations of the same motive as Grothendieck, who is the pioneer of the field responsible for many of the basic notions and visions, expressed it.

Cohomology requires a definition of integral for forms for all number fields. In p-adic context the lack of well-ordering of p-adic numbers implies difficulties both in homology and cohomology since the notion of boundary does not exist in topological sense. The notion of definite integral is problematic for the same reason. This has led to a proposal of reducing integration to Fourier analysis working for symmetric spaces but requiring algebraic extensions of p-adic numbers and an appropriate definition of the p-adic symmetric space. The definition is not unique and the interpretation is in terms of the varying measurement resolution.

The notion of infinite has gradually turned out to be more and more important for quantum TGD. Infinite primes, integers, and rationals form a hierarchy completely analogous to a hierarchy of second quantization for a super-symmetric arithmetic quantum field theory. The simplest infinite primes representing elementary particles at given level are in one-one correspondence with many-particle states of the previous level. More complex infinite primes have interpretation in terms of bound states.

- What makes infinite primes interesting from the point of view of algebraic geometry is that
infinite primes, integers and rationals at the n:th level of the hierarchy are in 1-1 correspondence with rational functions of n arguments. One can solve the roots of associated polynomials and perform a root decomposition of infinite primes at various levels of the hierarchy and assign to them Galois groups acting as automorphisms of the field extensions of polynomials defined by the roots coming as restrictions of the basic polynomial to planes x
_{n}=0, x_{n}=x_{n-1}=0, etc... - These Galois groups are suggested to define non-commutative generalization of homotopy and homology theories and non-linear boundary operation for which a geometric interpretation in terms of the restriction to lower-dimensional plane is proposed. The Galois group G
_{k}would be analogous to the relative homology group relative to the plane x_{k-1}=0 representing boundary and makes sense for all number fields also geometrically. One can ask whether the invariance of the complex of groups under the permutations of the orders of variables in the reduction process is necessary. Physical interpretation suggests that this is not the case and that all the groups obtained by the permutations are needed for a full description. - The algebraic counterpart of boundary map would map the elements of G
_{k}identified as analog of homotopy group to the commutator group [G_{k-2},G_{k-2}] and therefore to the unit element of the abelianized group defining cohomology group. In order to obtains something analogous to the ordinary homology and cohomology groups one must however replaces Galois groups by their group algebras with values in some field or ring. This allows to define the analogs of homotopy and homology groups as their abelianizations. Cohomotopy, and cohomology would emerge as duals of homotopy and homology in the dual of the group algebra. - That the algebraic representation of the boundary operation is not expected to be unique turns into blessing when on keeps the TGD as almost topological QFT vision as the guide line. One can include all boundary homomorphisms subject to the condition that the anticommutator δ
^{i}_{k}δ^{j}_{k-1}+δ^{j}_{k}δ^{i}_{k-1}maps to the group algebra of the commutator group [G_{k-2},G_{k-2}]. By adding dual generators one obtains what looks like a generalization of anticommutative fermionic algebra and what comes in mind is the spectrum of quantum states of a SUSY algebra spanned by bosonic states realized as group algebra elements and fermionic states realized in terms of homotopy and cohomotopy and in abelianized version in terms of homology and cohomology. Galois group action allows to organize quantum states into multiplets of Galois groups acting as symmetry groups of physics. Poincare duality would map the analogs of fermionic creation operators to annihilation operators and vice versa and the counterpart of pairing of k:th and n-k:th homology groups would be inner product analogous to that given by Grassmann integration. The interpretation in terms of fermions turns however to be wrong and the more appropriate interpretation is in terms of Dolbeault cohomology applying to forms with homomorphic and antiholomorphic indices. - The intuitive idea that the Galois group is analogous to 1-D homotopy group which is the only non-commutative homotopy group, the structure of infinite primes analogous to the braids of braids of braids of ... structure, the fact that Galois group is a subgroup of permutation group, and the possibility to lift permutation group to a braid group suggests a representation as flows of 2-D plane with punctures giving a direct connection with topological quantum field theories for braids, knots and links. The natural assumption is that the flows are induced from transformations of the symplectic group acting on δ M
^{2}_{+/-}× CP_{2}representing quantum fluctuating degrees of freedom associated with WCW ("world of classical worlds"). Discretization of WCW and cutoff in the number of modes would be due to the finite measurement resolution. The outcome would be rather far reaching: finite measurement resolution would allow to construct WCW spinor fields explicitly using the machinery of number theory and algebraic geometry. - A connection with operads is highly suggestive. What is nice from TGD perspective is that the non-commutative generalization homology and homotopy has direct connection to the basic structure of quantum TGD almost topological quantum theory where braids are basic objects and also to hyper-finite factors of type II
_{1}. This notion of Galois group makes sense only for the algebraic varieties for which coefficient field is algebraic extension of some number field. Braid group approach however allows to generalize the approach to completely general polynomials since the braid group make sense also when the ends points for the braid are not algebraic points (roots of the polynomial).

This construction would realize the number theoretical, algebraic geometrical, and topological content in the construction of quantum states in TGD framework in accordance with TGD as almost TQFT philosophy, TGD as infinite-D geometry, and TGD as generalized number theory visions.

*2. p-Adic integration and cohomology*

This picture leads also to a proposal how p-adic integrals could be defined in TGD framework.

- The calculation of twistorial amplitudes reduces to multi-dimensional residue calculus. Motivic integration gives excellent hopes for the p-adic existence of this calculus and braid representation would give space-time representation for the residue integrals in terms of the braid points representing poles of the integrand: this would conform with quantum classical correspondence. The power of 2π appearing in multiple residue integral is problematic unless it disappears from scattering amplitudes. Otherwise one must allow an extension of p-adic numbers to a ring containing powers of 2π.
- Weak form of electric-magnetic duality and the general solution ansatz for preferred extremals reduce the Kähler action defining the Kähler function for WCW to the integral of Chern-Simons 3-form. Hence the reduction to cohomology takes places at space-time level and since p-adic cohomology exists there are excellent hopes about the existence of p-adic variant of Kähler action. The existence of the exponent of Kähler gives additional powerful constraints on the value of the Kähler fuction in the intersection of real and p-adic worlds consisting of algebraic partonic 2-surfaces and allows to guess the general form of the Kähler action in p-adic context.
- One also should define p-adic integration for vacuum functional at the level of WCW. p-Adic thermodynamics serves as a guideline leading to the condition that in p-adic sector exponent of Kähler action is of form (m/n)
^{r}, where m/n is divisible by a positive power of p-adic prime p. This implies that one has sum over contributions coming as powers of p and the challenge is to calculate the integral for K= constant surfaces using the integration measure defined by an infinite power of Kähler form of WCW reducing the integral to cohomology which should make sense also p-adically. The p-adicization of the WCW integrals has been discussed already earlier using an approach based on harmonic analysis in symmetric spaces and these two approaches should be equivalent. One could also consider a more general quantization of Kähler action as sum K=K_{1}+K_{2}where K_{1}=rlog(m/n) and K_{2}=n, with n divisible by p since exp(n) exists in this case and one has exp(K)= (m/n)^{r}× exp(n). Also transcendental extensions of p-adic numbers involving n+p-2 powers of e^{1/n}can be considered. - If the Galois group algebras indeed define a representation for WCW spinor fields in finite measurement resolution, also WCW integration would reduce to summations over the Galois groups involved so that integrals would be well-defined in all number fields.

*3. Floer homology, Gromov-Witten invariants, and TGD*

Floer homology defines a generalization of Morse theory allowing to deduce symplectic homology groups
by studying Morse theory in loop space of the symplectic manifold. Since the symplectic transformations of the boundary of δ M^{4}_{+/-}× CP_{2} define isometry group of WCW, it is very natural to expect that Kähler action defines a generalization of the Floer homology allowing to understand the symplectic aspects of quantum TGD. The hierarchy of Planck constants implied by the one-to-many correspondence between canonical momentum densities and time derivatives of the imbedding space coordinates leads naturally to singular coverings of the imbedding space and the resulting symplectic Morse theory could characterize the homology of these coverings.

One ends up to a more precise definition of vacuum functional: Kähler action reduces Chern-Simons terms (imaginary in Minkowskian regions and real in Euclidian regions) so that it has both phase and real exponent which makes the functional integral well-defined. Both the phase factor and its conjugate must be allowed and the resulting degeneracy of ground state could allow to understand qualitatively the delicacies of CP breaking and its sensitivity to the parameters of the system. The critical points with respect to zero modes correspond to those for Kähler function. The critical points with respect to complex coordinates associated with quantum fluctuating degrees of freedom are not allowed by the positive definiteness of Kähler metric of WCW. One can say that Kähler and Morse functions define the real and imaginary parts of the exponent of vacuum functional.

The generalization of Floer homology inspires several new insights. In particular, space-time surface as hyper-quaternionic surface could define the 4-D counterpart for pseudo-holomorphic 2-surfaces in Floer homology. Holomorphic partonic 2-surfaces could in turn correspond to the extrema of Kähler function with respect to zero modes and holomorphy would be accompanied by super-symmetry.

Gromov-Witten invariants appear in Floer homology and topological string theories and this inspires the attempt to build an overall view about their role in TGD. Generalization of topological string theories of type A and B to TGD framework is proposed. The TGD counterpart of the mirror symmetry would be the equivalence of formulations of TGD in H=M^{4}× CP_{2} and in CP_{3}× CP_{3} with space-time surfaces replaced with 6-D sphere bundles.

*4. K-theory, branes, and TGD *

K-theory and its generalizations play a fundamental role in super-string models and M-theory since they allow a topological classification of branes. After representing some physical objections against the notion of brane more technical problems of this approach are discussed briefly and it is proposed how TGD allows to overcome these problems. A more precise formulation of the weak form of electric-magnetic duality emerges: the original formulation was not quite correct for space-time regions with Euclidian signature of the induced metric. The question about possible TGD counterparts of R-R and NS-NS fields and S, T, and U dualities is discussed.

*5. p-Adic space-time sheets as correlates for Boolean cognition*

p-Adic physics is interpreted as physical correlate for cognition. The so called Stone spaces are in one-one correspondence with Boolean algebras and have typically 2-adic topologies. A generalization to p-adic case with the interpretation of p pinary digits as physically representable Boolean statements of a Boolean algebra with 2^{n}>p>p^{n-1} statements is encouraged by p-adic length scale hypothesis. Stone spaces are synonymous with profinite spaces about which both finite and infinite Galois groups represent basic examples. This provides a strong support for the connection between Boolean cognition and p-adic space-time physics. The Stone space character of Galois groups suggests also a deep connection between number theory and cognition and some arguments providing support for this vision are discussed.

[55] **viXra:1111.0088 [pdf]**
*replaced on 2012-01-30 08:34:19*

**Authors:** Matti Pitkänen

**Comments:** 17 Pages.

Witten was awarded by Fields medal from a construction recipe of Jones polynomial based on topological QFT assigned with braids and based on Chern-Simons action. Recently Witten has been working with an attempt to understand in terms of quantum theory the so called Khovanov polynomial associated with a much more abstract link invariant whose interpretation and real understanding remains still open.

The attempts to understand Witten's thoughts lead to a series of questions unavoidably culminating to the frustrating "Why I do not have the brain of Witten making perhaps possible to answer these questions?". This one must just accept. In this article I summarize some thoughts inspired by the associations of the talk of Witten with quantum TGD and with the model of DNA as topological quantum computer. In my own childish manner I dare believe that these associations are interesting and dare also hope that some more brainy individual might take them seriously.

An idea inspired by TGD approach which also main streamer might find interesting is that the Jones invariant defined as vacuum expectation for a Wilson loop in 2+1-D space-time generalizes to a vacuum expectation for a collection of Wilson loops in 2+2-D space-time and could define an invariant for 2-D knots and for cobordisms of braids analogous to Jones polynomial. As a matter fact, it turns out that a generalization of gauge field known as gerbe is needed and that in TGD framework classical color gauge fields defined the gauge potentials of this field. Also topological string theory in 4-D space-time could define this kind of invariants. Of course, it might well be that this kind of ideas have been already discussed in literature.

[54] **viXra:1111.0086 [pdf]**
*replaced on 2012-01-30 08:45:30*

**Authors:** Matti Pitkänen

**Comments:** 61 Pages.

There have been impressive steps in the understanding of N=4 maximally sypersymmetric YM theory possessing 4-D super-conformal symmetry. This theory is related by AdS/CFT duality to certain string theory in AdS_{5}× S^{5} background. Second stringy representation was discovered by Witten and is based on 6-D Calabi-Yau manifold defined by twistors. The unifying proposal is that so called Yangian symmetry is behind the mathematical miracles involved.

In the following I will discuss briefly the notion of Yangian symmetry and suggest its generalization in TGD framework by replacing conformal algebra with appropriate super-conformal algebras. Also a possible realization of twistor approach and the construction of scattering amplitudes in terms of Yangian invariants defined by Grassmannian integrals is considered in TGD framework and based on the idea that in zero energy ontology one can represent massive states as bound states of massless particles. There is also a proposal for a physical interpretation of the Cartan algebra of Yangian algebra allowing to understand at the fundamental level how the mass spectrum of n-particle bound states could be understood in terms of the n-local charges of the Yangian algebra.

Twistors were originally introduced by Penrose to characterize the solutions of Maxwell's equations. Kähler action is Maxwell action for the induced Kähler form of CP_{2}. The preferred extremals allow a very concrete interpretation in terms of modes of massless non-linear field. Both conformally compactified Minkowski space identifiable as so called causal diamond and CP_{2} allow a description in terms of twistors. These observations inspire the proposal that a generalization of Witten's twistor string theory relying on the identification of twistor string world sheets with certain holomorphic surfaces assigned with Feynman diagrams could allow a formulation of quantum TGD in terms of 3-dimensional holomorphic surfaces of CP_{3}× CP_{3} mapped to 6-surfaces dual CP_{3}× CP_{3}, which are sphere bundles so that they are projected in a natural manner to 4-D space-time surfaces. Very general physical and mathematical arguments lead to a highly unique proposal for the holomorphic differential equations defining the complex 3-surfaces conjectured to correspond to the preferred extremals of Kähler action.

[53] **viXra:1111.0085 [pdf]**
*replaced on 2012-03-16 03:44:46*

**Authors:** Matti Pitkänen

**Comments:** 17 Pages.

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II_{1} (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λ_{i}) for a positive integer valued variable n characterized by rational-valued parameters λ_{i} is obtained by replacing n and the integers characterizing λ_{i} with so called quantum integers depending on the quantum phase q_{m}=exp(i2π/m). Quantum integer n_{q} must be defined as the product of quantum counterparts p_{q} of the primes p appearing in the prime decomposition of n. One has p_{q}= sin(2π p/m)/sin(2π/m) for p≠ P and p_{q}=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers P^{n} to P^{-n} and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ P_{n})=∑ I(P_{n}). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n^{+}n^{-}, n^{+}_{q}>0 with fixed n^{-}_{q}<0,
are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ k_{p}Δ R/R and Δ m/m≈ k_{m}Δ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

[52] **viXra:1111.0085 [pdf]**
*replaced on 2012-01-30 08:52:00*

**Authors:** Matti Pitkänen

**Comments:** 17 Pages.

Shnoll and collaborators have discovered strange repeating patterns of random fluctuations of physical observables such as the number n of nuclear decays in a given time interval. Periodically occurring peaks for the distribution of the number N(n) of measurements producing n events in a series of measurements as a function of n is observed instead of a single peak. The positions of the peaks are not random and the patterns depend on position and time varying periodically in time scales possibly assignable to Earth-Sun and Earth-Moon gravitational interaction.

These observations suggest a modification of the expected probability distributions but it is very difficult to imagine any physical mechanism in the standard physics framework. Rather, a universal deformation of predicted probability distributions would be in question requiring something analogous to the transition from classical physics to quantum physics.

The hint about the nature of the modification comes from the TGD inspired quantum measurement theory proposing a description of the notion of finite measurement resolution in terms of inclusions of so called hyper-finite factors of type II_{1} (HFFs) and closely related quantum groups. Also p-adic physics -another key element of TGD- is expected to be involved. A modification of a given probability distribution P(nkenovert λ_{i}) for a positive integer valued variable n characterized by rational-valued parameters λ_{i} is obtained by replacing n and the integers characterizing λ_{i} with so called quantum integers depending on the quantum phase q_{m}=exp(i2π/m). Quantum integer n_{q} must be defined as the product of quantum counterparts p_{q} of the primes p appearing in the prime decomposition of n. One has p_{q}= sin(2π p/m)/sin(2π/m) for p≠ P and p_{q}=P for p=P. m must satisfy m≥ 3, m≠ p, and m≠ 2p.

The quantum counterparts of positive integers can be negative. Therefore quantum distribution is defined first as p-adic valued distribution and then mapped by so called canonical identification I to a real distribution by the map taking p-adic -1 to P and powers P^{n} to P^{-n} and other quantum primes to themselves and requiring that the mean value of n is for distribution and its quantum variant. The map I satisfies I(∑ P_{n})=∑ I(P_{n}). The resulting distribution has peaks located periodically with periods coming as powers of P. Also periodicities with peaks corresponding to n=n^{+}n^{-}, n^{+}_{q}>0 with fixed n^{-}_{q}<0,
are predicted. These predictions are universal and easily testable. The prime P and integer m characterizing the quantum variant of distribution can be identified from data. The shapes of the distributions obtained are qualitatively consistent with the findings of Shnoll but detailed tests are required to see whether the number theoretic predictions are correct.

The periodic dependence of the distributions would be most naturally assignable to the gravitational interaction of Earth with Sun and Moon and therefore to the periodic variation of Earth-Sun and Earth-Moon distances. The TGD inspired proposal is that the p-dic prime P and integer m characterizing the quantum distribution are determined by a process analogous to a state function reduction and their most probably values depend on the deviation of the distance R through the formulas Δ p/p≈ k_{p}Δ R/R and Δ m/m≈ k_{m}Δ R/R. The p-adic primes assignable to elementary particles are very large unlike the primes which could characterize the empirical distributions. The hierarchy of Planck constants allows the gravitational Planck constant assignable to the space-time sheets mediating gravitational interactions to have gigantic values and this allows p-adicity with small values of the p-adic prime P.

[51] **viXra:1111.0026 [pdf]**
*replaced on 2014-04-10 07:09:16*

**Authors:** Malcolm Macleod

**Comments:** 3 Pages.

Proposed is a geometrical formula for a dimensionless magnetic monopole constructed from Planck time, elementary charge, -c and alpha, the fine structure constant. A formula for the electron may be constructed from these monopoles, this formula suggests that the charge distribution of the electron is perfectly symmetrical. As this monopole comprises a 1/3rd part of electron charge, it is analogous to the quark which in turn suggests that the basis for all charge is this monopole, consequently, although charges may have opposite polarity, their magnitudes must be equivalent, the differences between the proton and electron for example being geometrical rather than physical. A temperature particle labeled the 'kelvon' is proposed. Furthermore, these formulas suggest a Mathematical Universe constructed from Planck units, wave-particle duality becoming a wave-state to Planck point-state oscillation.

**Category:** Mathematical Physics

[50] **viXra:1110.0030 [pdf]**
*replaced on 2012-05-16 03:31:46*

**Authors:** Dan Visser

**Comments:** 13 Pages.

Version2 is written after my paper “Duonistic Neutrinos Violate Relativity”. A theoretical calculation with a new dark energy force formula discloses the correctness of the experimental faster-than-light-neutrinos in the CERN-San Grasso experiment. The formulation in this paper theoretically confirms that Einstein’s Relativity could be violated. This introduces the obligation to accept a new cosmological model, called the Double Torus hypothesis . The theoretical calculation in this paper is based on a new momentum of dark energy force. This paper theoretically calculates 62.8 nanosecond for the experimental detected early-arrival of muon-neutrinos related to how light-in-vacuum would have arrived. This is a marvelous close match compared to the ((60.7 ± 6.9 (stat.) ± 7.4 (sys.)) nanosecond found during the ‘neutrino-flight path’ from CERN to San Grasso in the OPERA-project. However, this version-2 paper also makes clear neutrinos can only go faster-than-light in neutrino-pairs: I call these pairs Duonistic Neutrinos! Just as in the paper “Duonistic Neutrinos Violate Relativity”. This paper presents the set of equations to prove that.

**Category:** Mathematical Physics

[49] **viXra:1108.0005 [pdf]**
*replaced on 2012-04-20 10:27:21*

**Authors:** DT Froedge

**Comments:** 13 Pages. Clarifying some points of previous version

In a previous paper we have discussed the conjecture of a variable particle rest mass as a function of gravitational potential [1]. This paper discuses the implications, in regard to a large neutron star, and contrast the difference between the predicted phenomena, and Black Hole theory as put fourth by standard GR. As most know, Einstein was not convinced of the existence of Black Holes, but modern solutions of the GR field equations appear to agree with the experimental evidence. There are some problems however, as are well known, the explanations for the diffuse, and the persistent source gamma ray emissions from the galactic center, do not have an adequate explanation, and the energy engines driving Quasars and AGNs are not sufficiently explained. This paper will explore the differences between VRM neutron stars, and Black Holes, for the purpose of identifying detectable, and measurable phenomena. The validity of this theory will be established on the finding of massive neutron stars or massive pulsars. >3 suns.

**Category:** Mathematical Physics

[48] **viXra:1106.0018 [pdf]**
*replaced on 23 Jun 2011*

**Authors:** Sergey V. Ershkov

**Comments:** 9 pages

Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.

**Category:** Mathematical Physics

[47] **viXra:1106.0018 [pdf]**
*replaced on 20 Jun 2011*

**Authors:** Sergey V. Ershkov

**Comments:** 7 pages

Here is presented a new exact solution of Ice dynamics in Glaciers in terms of viscousplastic
theory of movements, for 2-dimensional case: x (t) = y (t). In general case, 2-D
solution of Ice dynamics could be classified as Riccati's type. Due to a very special
character of Riccati's type equation, it's general solution is proved to have a proper gap
of components of such a solution.

**Category:** Mathematical Physics

[46] **viXra:1105.0022 [pdf]**
*replaced on 2013-05-13 17:01:06*

**Authors:** Dan Visser

**Comments:** 5 Pages.

This paper shows how my ‘dark energy force formula’ emerges five more space- and two more time-dimensions in nature. The ‘formula’ is earlier described in vixra-papers, announcing the universe is a Double Torus of dark energy and dark matter. The ‘formula’ represents a completely different force than the cosmological constant of Einstein, which is used to explain the accelerated expansion in Big Bang cosmology. With this in mind, two independent experimental investigations have given additional proof for my ‘dark energy force formula’, as follows: 1) The ratio of five extra space-dimensions and two extra time dimensions represent the up- and down electron-spin, behaving in a ‘chessboard-structure’ and associated with grapheme-experiments. 2) A computer-simulation shows a Double Torus, artificially emerging from two colliding black-holes. These results match with my hypothesis that the universe indeed is a Double Torus of dark energy and dark matter, because my (new) ’dark energy force formula‘ matches these two investigations. This (new) force could therefore have a link to topological insulators to guide light without scattering in quantum-computers.

**Category:** Mathematical Physics

[45] **viXra:1104.0085 [pdf]**
*replaced on 2014-01-07 10:17:53*

**Authors:** Dan Visser

**Comments:** 7 Pages. Version-3 removed mistakes in interpretation.

In version-1 for the first time an announcement was made in this paper to have found fundamental evidence for the flyby-anomalies of six satellites earlier investigated by John Anderson and co-workers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The central part of this theoretical evidence exists of a ‘dark matter flow’ being the cause of a velocity-change for satellites during their ‘flyby’ along the earth. A formula is given to calculate the velocity-change caused by the dark matter flow. The origin of the evidence is related to a ‘dark energy force formula‘, which is a new force in a new proposed cosmological model describing dark energy and dark matter in a double torus geometry. Version-2 replaces version-1, because I read about new investigation of GPS satellites, which predict dark matter surrounding the earth-equator. In version-2 I cleared an expression without an effect on the original end-result of version-1 and I extended it with the calculation of the energy satellites are feeling from dark matter around the earth-equator. Version-3 makes much better clear that satellites can be used to calculate the dark energy density flow around the earth-equator from the perspective of a new cosmological model: The Double Torus Universe.

**Category:** Mathematical Physics

[44] **viXra:1104.0085 [pdf]**
*replaced on 2014-01-06 16:48:19*

**Authors:** Dan Visser

**Comments:** 7 Pages.

In version-1 for the first time an announcement was made in this paper to have found fundamental evidence for the flyby-anomalies of six satellites earlier investigated by John Anderson and co-workers of the Jet Propulsion Laboratory (JPL) in Pasadena USA. The central part of this theoretical evidence exists of a ‘dark matter flow’ being the cause of a velocity-change for satellites during their ‘flyby’ along the earth. A formula is given to calculate the velocity-change caused by the dark matter flow. The origin of the evidence is related to a ‘dark energy force formula‘, which is a new force in a new proposed cosmological model describing dark energy and dark matter in a double torus geometry. Version-2 replaces version-1, because I read about new investigation of GPS satellites, which predict dark matter surrounding the earth-equator. In version-2 I cleared an expression without an effect on the original end-result of version-1 and I extended it with the calculation of the energy satellites are feeling from dark matter around the earth-equator.

**Category:** Mathematical Physics

[43] **viXra:1103.0115 [pdf]**
*replaced on 2012-04-11 06:16:58*

**Authors:** José Francisco García Juliá

**Comments:** 5 Pages.

We consider that the action at a distance is carried out by virtual carriers of the force,
which are created and annihilated in the vacuum by the field in a time less than that of
the Heisenberg's uncertainty.

**Category:** Mathematical Physics

[42] **viXra:1103.0115 [pdf]**
*replaced on 2012-02-14 08:13:39*

**Authors:** José Francisco García Juliá

**Comments:** 5 Pages.

We consider that the action at a distance is carried out by virtual carriers of the force,
which are created and annihilated in the vacuum by the field in a time less than that of
the Heisenberg's uncertainty.

**Category:** Mathematical Physics

[41] **viXra:1103.0115 [pdf]**
*replaced on 2012-01-26 10:29:23*

**Authors:** José Francisco García Juliá

**Comments:** 3 Pages.

**Category:** Mathematical Physics

[40] **viXra:1103.0012 [pdf]**
*replaced on 2013-06-26 16:43:29*

**Authors:** Dan Visser

**Comments:** 7 Pages. version 2 removes a ommission the notation of the formula, however renewed analysis implies no change in calculated results

This paper announces dark energy to be measured as a cosmic microwave background frame in the Double Torus hypothesis. This Double Torus (CMB)-frame is related to a specific quantum-state of dark energy and dark matter. In addition this paper also refers to a planned dark energy interferometer-project, which is expected to be operational in 2014. Both aspects can be combined in order to get a better expectation and interpretation of the detection of dark energy. This paper has motivated me to calculate a specific value for the Double Torus dark energy. The calculated value is about 4 x 10^-114 [X.s] in 6.4 x 10^-48 [m^2]. A new kind of spin-quantum-state [X.s] is introduced as a property of dark energy in the Double Torus. Probably this paper might be of interest to the dark energy interferometer-project. It surely is of importance for the discrepancy that exists in vacuum energy density.

**Category:** Mathematical Physics

[39] **viXra:1102.0032 [pdf]**
*replaced on 3 Oct 2011*

**Authors:** Malcolm Macleod

**Comments:**
3 pages. v1 in Russian, v4 in English

The natural constants, G; h; e, μ_{0} and m_{e} are presented as geometrical shapes in terms
of Planck momentum, α (Sommerfeld fine structure constant) and c. A square root
solution of Planck momentum denoted Quintessence-momentum Q links the mass and
charge constants. The electron formula describes a dimensionless magnetic monopole.
The Rydberg constant R1, the most accurate of the natural constants, is used for crossreference,
the solutions are consistent with CODATA 2010 precision.

**Category:** Mathematical Physics

[38] **viXra:1102.0032 [pdf]**
*replaced on 18 May 2011*

**Authors:** Malcolm Macleod

**Comments:**
3 pages. v1 in Russian, v3 in English

A mathematical description of the natural constants, G, h, e, μ_{0} m_{e} R_{∞}, is presented in
terms of momentum Q, alpha (Sommerfeld fine structure constant) and c. This momentum
is referred to as Quintessence-momentum and is the square root of Planck
momentum. The formulas describe geometrical forms, the units are consistent with
corresponding SI units and the numerical values, including the Rydberg constant and
the vacuum permeability, are consistent with CODATA 2006.

**Category:** Mathematical Physics

[37] **viXra:1102.0032 [pdf]**
*replaced on 20 Feb 2011*

**Authors:** Malcolm Macleod

**Comments:**
3 pages. v1 in Russian, v2 in English

This paper suggests a 'quantity of momentum', a square root of Planck momentum,
here referred to as Quintessence-momentum, as a natural unit that is common to both
mass and charge. In terms of this Quintessence momentum Q, alpha (Sommerfeld fine
structure constant) and c; geometrical formulas for the natural physical constants and
the electron mass are proposed. Results are consistent with CODATA 2006.

**Category:** Mathematical Physics

[36] **viXra:1102.0027 [pdf]**
*replaced on 2012-09-06 04:35:29*

**Authors:** Sergey G. Fedosin

**Comments:** 5 Pages. Turkish Journal of Physics, 2012, Vol. 36, No 3, P. 461 – 464.

The scale dimension discovered in the theory of infinite nesting of matter is studied from the perspective of physical implementation of well-studied four-and n-dimensional geometric objects. Adding the scale dimension to Minkowski four-dimensional space means the necessity to use the five-dimensional spacetime.

**Category:** Mathematical Physics

[35] **viXra:1102.0027 [pdf]**
*replaced on 18 Feb 2011*

**Authors:** Sergey G. Fedosin

**Comments:**
4 pages. v1 in Russian, v2 in English

The scale dimension which is discovered in the theory of infinite nesting of matter is studied from the
perspective of the physical implementation of well-studied four-and n-dimensional geometric objects.
Adding of the scale dimension to Minkowski space means the need to use the five-dimensional spacetime.

**Category:** Mathematical Physics

[34] **viXra:1101.0037 [pdf]**
*replaced on 12 Jan 2011*

**Authors:** Ke Xiao

**Comments:** 5 pages

The fine structure constant α = e^{2}/hc ~ 1/137.036 and the blackbody
radiation constant α_{R} = e^{2}(a_{R}/k^{4}_{B})^{1/3} ~ 1/157.555
are linked by prime numbers. The blackbody radiation constant is a new method to measure
the fine structure constant. It also links the fine structure constant to the
Boltzmann constant.

**Category:** Mathematical Physics

[33] **viXra:1012.0052 [pdf]**
*replaced on 17 Jan 2011*

**Authors:** Giuliano Bettini

**Comments:** 9 pages, v3 in Italian, v2 in English, corrections to the tables, and a new table added.

There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.

**Category:** Mathematical Physics

[32] **viXra:1012.0052 [pdf]**
*replaced on 1 Jan 2011*

**Authors:** Giuliano Bettini

**Comments:** 9 pages, v1 in Italian, v2 in English, corrections to the tables, and a new table added.

There are 32 possible combinations of symmetry operations that define the external symmetry of
crystals. These 32 possible combinations result in the 32 crystal classes.
But for a radar engineer it is inevitable to associate "32" to "5 bits".
I submit a tentative classification of the 32 crystal classes with a 5 bit classification, obviously with
a (tentative) physical meaning of each bit.
Each bit means a physical property.

**Category:** Mathematical Physics

[31] **viXra:1012.0031 [pdf]**
*replaced on 16 Dec 2010*

**Authors:** Elemér E Rosinger

**Comments:** 9 pages

A class of non-Cartesian physical systems, [7], are those whose
composite state spaces are given by significantly extended tensor products.
A more detailed presentation of the way such extended tensor products
are constructed is offered, based on a step by step comparison with the
construction of usual tensor products. This presentation clarifies the
extent to which the extended tensor products are indeed more general
than the usual ones.

**Category:** Mathematical Physics

[30] **viXra:1010.0014 [pdf]**
*replaced on 1 Jun 2011*

**Authors:** Dan Visser

**Comments:** 5 pages

A new cosmological model, named the Twin-Tori Model (TTM)[1], postulates a
dark energy force F_{de} , which empowers the dynamic of a lower order universe, well
known as the big bang. In this paper I introduce the 1st derivative F'_{de} of this dark energy
force to reveal deeper properties of the TTM, such as: why quantummechanics exists in
the big bang, why dark matter and visible matter are equally responsible for gravity in
galaxies for 1/4 of the density of dark matter at a specific length, why the big bang universe
is recalculated by subquantumlevel-information below the Plancklength, and why the
impression of space-expansion is due to the higher order cosmological model TTM.

**Category:** Mathematical Physics

[29] **viXra:1010.0013 [pdf]**
*replaced on 2013-11-25 09:05:44*

**Authors:** Dan Visser

**Comments:** 11 Pages. Version-3 is only textual modified and not mathematically altered. It services a better understanding of the beginning of the Double Torus framework.

A (new) ‘dark energy force-formula’ was introduced on April 10 2004 by Dan Visser, Almere, the Netherlands on his website (reference 1a). The (new) formula was picked up by a PhD-mathematician and -Physics, Christopher Forbes (UK), in the summer of 2009, leading to email-contact among them, and resulting in a publication of a general mathematical expression, whereof Dan’s (new) ‘dark energy force-formula’ indeed resulted from the general expressing (reference 2). Additional an amount of (new) dark energy resulted too. Afterwards Dan published his derivation of the (new) force in the Vixra-archive on October 7 2010 (in retrospective). He called his mathematical exercises a ‘thought-experiment’. That had as result the (new) ‘dark energy force-formula’. In the versions following (version-2 and -3) only textual changes were made for servicing a better understanding of the thought-experiment, of course without altering the original mathematical content. Further development was focussed on working–out the (new) dynamics in the Double Torus hypothesis. This is a hypothesis that claims the Big Bang cosmology can no longer be maintained as the model for the universe. The main issue in ‘Dan’s-thought-experiment’ is a scaling-away-principle’,which is characterized by ‘scaling-away’ two black holes from each other (small and large), as well as ‘melting them together’ and making them ‘temperature connected’. Then an observer would receive the same evaporation-radiation from both black holes at the same time. These three exercises (scaling-away, melting-together and temperature-connection) had the aim to keep entropy conserved in the universe. However, ‘scaling-away’ causes a ‘change of dark information’ at the surface of one or the other black hole. Such a change had to correspond to a ‘new force’. That was further exercised, analyzed, synthesized, combined and translated as a mathematical thought-experiment. The result: Dan’s (new) ‘dark energy force-formula’.

**Category:** Mathematical Physics

[28] **viXra:1010.0013 [pdf]**
*replaced on 2013-01-02 15:57:11*

**Authors:** Dan Visser

**Comments:** 12 Pages.

A (new) ‘dark energy force-formula’ was introduced on April 10 2004 on Dan Visser’s website. His (new) formula was picked up by a PhD-mathematician and - Physics, Christopher Forbes (UK) in the summer of 2009, leading to email-contact among them, and resulting in a publication of a general mathematical expression, whereof Dan Visser’s (new) ‘dark energy force-formula’ came out as a solution. The derivation of this (new) force was then published in the Vixra-archive on October 7 2010 (in retrospective). The ‘thought-experiment’ is described as a mathematical exercise, which in the end is expressed as Dan Visser's (new) ‘dark energy force-formula’. Since then only textual changes were made for the benefit of a better explanation of the hypothesis, without altering the original mathematical content. The main issue in the ‘thought-experiment’ is a ‘non-relativistic scaling principle’, characterized as ‘scaling-away’ two black holes from each other (small and large), as well as ‘melting them together’. Both ‘movements’ presents a ‘change of dark information’. This was further analyzed, synthesized, combined and translated mathematically by Dan Visser, into a force of ‘extra time’ hitting an observer’s eye. The result is the (new) ‘dark energy force’, a ‘non-relativistic force’.

**Category:** Mathematical Physics

[27] **viXra:1009.0047 [pdf]**
*replaced on 2013-05-03 15:35:33*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 20 Pages.

•ABSTRACT: We study a generalization of the zeta regularization method applied to the case of the regularization of divergent integrals for positive ‘s’ , using the Euler Maclaurin summation formula, we manage to express a divergent integral in term of a linear combination of divergent series , these series can be regularized using the Riemann Zeta function s >0 , in the case of the pole at s=1 we use a property of the Functional determinant to obtain the regularization , with the aid of the Laurent series in one and several variables we can extend zeta regularization to the cases of integrals , we believe this method can be of interest in the regularization of the divergent UV integrals in Quantum Field theory since our method would not have the problems of the Analytic regularization or dimensional regularization
•Keywords: = Riemann Zeta function, Functional determinant, Zeta regularization, divergent series .

**Category:** Mathematical Physics

[26] **viXra:1009.0007 [pdf]**
*replaced on 2012-03-21 15:41:57*

**Authors:** DT Froedge

**Comments:** 36 Pages. V032112 ongoing

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are, and single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by then by defining an action field based on the endpoint action of the particles in the system, develop a solution which properly illustrates internal dynamics as well as particle interactions. The complete function has both real, and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle masses are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent parts of the Systemfunction. A clear relation between the classical and quantum properties of particles is made, increasing the scope of QM.

**Category:** Mathematical Physics

[25] **viXra:1009.0007 [pdf]**
*replaced on 2012-03-11 13:10:52*

**Authors:** DT Froedge

**Comments:** 39 Pages. For presentation April 12 APS Atlanta Verson V012612 (ongoing)

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are approximations, and single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by then by defining an action field based on the endpoint action of the particles in the system, develop a solution which properly illustrates internal dynamics as well as particle interactions. The complete function has both real, and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle masses are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent parts of the Systemfunction. A clear relation between the classical and quantum properties of particles is made, increasing the scope of QM.

**Category:** Mathematical Physics

[24] **viXra:1009.0007 [pdf]**
*replaced on 2011-12-21 11:44:45*

**Authors:** DT Froedge

**Comments:** 39 Pages.

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. The basic concept is that there is a broader picture, based on a more general equation that includes the entire system of particles. The first part will be to postulate an equation, and then, by modifying the methods of Path Integrals, develop a solution which describes the internal dynamics as well as particle interactions of quantum particles. The complete function has both real and imaginary, as well as timelike and spacelike parts, each of which are separable into independent expressions that define particle properties. In the same manner that eigenvalues of the Schrödinger equation represents energy levels of an atomic system, particle are eigenvalues in an interacting universe of particles. The Dirac massive and massless equation and solution will be shown as factorable independent components. A clear distinction between the classical and quantum properties of particles is made, increasing the scope of QM.

**Category:** Mathematical Physics

[23] **viXra:1009.0007 [pdf]**
*replaced on 2 Jul 2011*

**Authors:** D.T. Froedge

**Comments:**
30 pages.

The purpose of this paper is to illustrate a fundamental, multiple particle, system equation for
which the Klein-Gordon-Dirac-Schrödinger equations are single particle special cases. In the
same manner that eigenvalues of the Schrödinger equation represents energy levels of an
interacting atomic system, eigenvalues represent particle energies in an interacting system of
particles. An equation and a solution is proposed that treats all of the particles in the universe
as a single system. The proposed solution is a descriptor of a symmetric, light speed
expanding group of interacting particles having familiar constituents.

**Category:** Mathematical Physics

[22] **viXra:1009.0007 [pdf]**
*replaced on 5 Mar 2011*

**Authors:** D.T. Froedge

**Comments:**
17 pages 38 equations 98kb

The purpose of this paper is to illustrate a fundamental, multiple particle,
system equation for which the Klein-Gordon-Dirac-Schrödinger equations are
single particle special cases. In the same manner that eigenvalues of the
Schrödinger equation represents energy levels of an interacting atomic system,
eigenvalues represent particle energies in an interacting system of particles. An
equation is proposed that has vector solutions defined in Dirac, or Clifford
algebra, that treats all of the particles in the universe as a single system. The
proposed solution is a descriptor of a symmetric, light speed expanding group
of interacting particles having real, as well as the familiar QM constituents.

**Category:** Mathematical Physics

[21] **viXra:1007.0005 [pdf]**
*replaced on 2012-11-22 05:57:29*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 12 Pages.

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the
Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in
one dimension
2
2 d V (x)
dx
- + for a real-valued function V(x) , this potential V is
related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units
where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian
operator will be the square of the imaginary part of the Riemann Zeros 2
n n E =g Also
trhough this paper we may refer to the Hamiltonian Operator whose Energies are the
square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same
case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to
simplify notation.
· Keywords: = Riemann Hypothesis, Functional determinant,

**Category:** Mathematical Physics

[20] **viXra:1007.0005 [pdf]**
*replaced on 2012-03-26 15:13:42*

**Authors:** Jose Javier Garicia Moreta

**Comments:** 25 Pages.

· ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the
Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in
one dimension
2
2 d V (x)
dx
- + for a real-valued function V(x) , this potential V is
related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units
where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian
operator will be the square of the imaginary part of the Riemann Zeros 2
n n E =g Also
trhough this paper we may refer to the Hamiltonian Operator whose Energies are the
square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same
case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to
simplify notation.
· Keywords: = Riemann Hypothesis, Functional determinant,

**Category:** Mathematical Physics

[19] **viXra:1007.0005 [pdf]**
*replaced on 2012-10-06 04:12:18*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 11 Pages.

• ABSTRACT: We give an spectral interpretation of the non-trivial zeros of the Riemann Xi-function. The main idea of the paper is to find a Hamiltonian (Hermitian) operator in the form with an even potential whose energies are precisely , the zeros of the Riemann Xi-function .
In order to obtain this Hamiltonian we use the WKB method and the Bohr-sommerfeld
quantization condition for the energies. We also prove the fact that the Riemann
Xi-function is proportional to the Functional determinant in the
sense of a zeta-regularized determinant
In this paper and for simplicity we use units so
• Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula ,Bolte’s law.

**Category:** Mathematical Physics

[18] **viXra:1007.0005 [pdf]**
*replaced on 2012-03-26 15:02:21*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 25 Pages.

ABSTRACT: We give a possible interpretation of the Xi-function of Riemann as the
Functional determinant det ( E - H ) for a certain Hamiltonian quantum operator in
one dimension
2
2 d V (x)
dx
- + for a real-valued function V(x) , this potential V is
related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units
where h =1 and that the mass is 2m =1.In this case the Energies of the Hamiltonian
operator will be the square of the imaginary part of the Riemann Zeros 2
n n E =g Also
trhough this paper we may refer to the Hamiltonian Operator whose Energies are the
square of the imaginary part of the Riemann Zeros as H or 2 H (square) in the same
case we will refer to the potential inside this Hamiltonian either as 2 V (x) or V (x) to
simplify notation.
· Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula , Quantum chaos.

**Category:** Mathematical Physics

[17] **viXra:1007.0005 [pdf]**
*replaced on 2012-01-25 05:58:47*

**Authors:** Jose Javier garcia

**Comments:** 25 Pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant
for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this
potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function,
through the paper we will assume that the reduced Planck constant is defined in units where and that the
mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part
of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are
the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to
the potential inside this Hamiltonian either as or to simplify notation.
Keywords: = Riemann Hypothesis, Functional determinant, WKB semiclassical
Approximation , Trace formula , Quantum chaos.

**Category:** Mathematical Physics

[16] **viXra:1007.0005 [pdf]**
*replaced on 2011-12-14 13:56:54*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 23 Pages. there is an ERROR, whenever it says 'Whose zeros' should we put 'Whose Energies' (A Hamiltonian has no zeros)H

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is .In this case the Energies of the Hamiltonian operator will be the square of the imaginary part of the Riemann Zeros Also trhough this paper we may refer to the Hamiltonian Operator whose Energies are the square of the imaginary part of the Riemann Zeros as or (square) in the same case we will refer to the potential inside this Hamiltonian either as or to simplify notation.

**Category:** Mathematical Physics

[15] **viXra:1007.0005 [pdf]**
*replaced on 2011-12-04 07:54:17*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 23 Pages.

We give a possible interpretation of the Xi-function of Riemann as the Functional determinant for a certain Hamiltonian quantum operator in one dimension for a real-valued function V(x) , this potential V is related to the half-integral of the logarithmic derivative for the Riemann Xi-function, through the paper we will assume that the reduced Planck constant is defined in units where and that the mass is

**Category:** Mathematical Physics

[14] **viXra:1006.0042 [pdf]**
*replaced on 2012-01-30 21:36:44*

**Authors:** Matti Pitkänen

**Comments:** 13 Pages.

This appendix contains basic facts about CP_{2} as a symmetric space and Kähler manifold. The
coding of the standard model symmetries to the geometry of CP_{2}, the physical interpretation of
the induced spinor connection in terms of electro-weak gauge potentials, and basic facts about
induced gauge fields are discussed

**Category:** Mathematical Physics

[13] **viXra:1006.0041 [pdf]**
*replaced on 2012-01-30 21:40:48*

**Authors:** Matti Pitkänen

**Comments:** 5 Pages.

The original justification for the hierarchy of Planck constants came from the indications that
Planck constant could have large values in both astrophysical systems involving dark matter and
also in biology. The realization of the hierarchy in terms of the singular coverings and possibly also
factor spaces of CD and CP_{2} emerged from consistency conditions. It however seems that TGD
actually predicts this hierarchy of covering spaces. The extreme non-linearity of the field equations
defined by Kähler action means that the correspondence between canonical momentum densities
and time derivatives of the imbedding space coordinates is 1-to-many. This leads naturally to the
introduction of the covering space of CD x CP_{2}, where CD denotes causal diamond defined as
intersection of future and past directed light-cones.

**Category:** Mathematical Physics

[12] **viXra:1006.0040 [pdf]**
*replaced on 2012-01-30 21:49:56*

**Authors:** Matti Pitkänen

**Comments:** 25 Pages.

The notion of electric magnetic duality emerged already two decades ago in the attempts to
formulate the Kähler geometry of the "world of classical worlds". Quite recently a considerable
step of progress took place in the understanding of this notion. This concept leads to the
identification of the physical particles as string like objects defined by magnetic charged wormhole
throats connected by magnetic
ux tubes. The second end of the string contains particle having
electroweak isospin neutralizing that of elementary fermion and the size scale of the string is
electro-weak scale would be in question. Hence the screening of electro-weak force takes place
via weak confinement. This picture generalizes to magnetic color confinement. Electric-magnetic
duality leads also to a detailed understanding of how TGD reduces to almost topological quantum
field theory. A surprising outcome is the necessity to replace CP_{2} Kähler form in Kähler action
with its sum with S^{2} Kähler form.

**Category:** Mathematical Physics

[11] **viXra:1006.0039 [pdf]**
*replaced on 2012-01-30 21:53:06*

**Authors:** Matti Pitkänen

**Comments:** 16 Pages.

Generalized Feynman diagrams have become the central notion of quantum TGD and one might even say that space-time surfaces can be identified as generalized Feynman diagrams. The challenge is to assign a precise mathematical content for this notion, show their mathematical existence, and develop a machinery for calculating them. Zero energy ontology has led to a dramatic progress in the understanding of generalized Feynman diagrams at the level of fermionic degrees of freedom. In particular, manifest finiteness in these degrees of freedom follows trivially from the basic identifications as does also unitarity and non-trivial coupling constant evolution. There are however several formidable looking challenges left.

- One should perform the functional integral over WCW degrees of freedom for fixed values of on mass shell momenta appearing in the internal lines. After this one must perform integral or summation over loop momenta.
- One must define the functional integral also in the p-adic context. p-Adic Fourier analysis relying on algebraic continuation raises hopes in this respect. p-Adicity suggests strongly that the loop momenta are discretized and ZEO predicts this kind of discretization naturally.

[10] **viXra:1006.0038 [pdf]**
*replaced on 2012-01-30 21:55:27*

**Authors:** Matti Pitkänen

**Comments:** 38 Pages.

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.

- The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis.
- Second part of the vision involves
hyper counterparts of the classical number fields
defined as subspaces of their complexifications
with Minkowskian signature of metric. Allowed space-time surfaces
would correspond to what might be called
hyper-quaternionic sub-manifolds of a
hyper-octonionic space and mappable to M
^{4}× CP_{2}in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content. - The third part of the vision involves infinite
primes identifiable in terms of an
infinite hierarchy of second quantized arithmetic
quantum fields theories on one hand, and as having
representations as space-time surfaces analogous to
zero loci of polynomials on the other hand.
Single space-time point would have
an infinitely complex structure since real unity can
be represented as a ratio of infinite numbers in
infinitely many manners each having its own number
theoretic anatomy. Single space-time point would be
in principle able to represent in its structure
the quantum state of the entire universe. This
number theoretic variant of Brahman=Atman identity
would make Universe an algebraic hologram.
Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.

Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.

**Category:** Mathematical Physics

[9] **viXra:1006.0038 [pdf]**
*replaced on 3 Nov 2010*

**Authors:** Matti Pitkänen

**Comments:** 695 Pages.

The focus of this book is the number theoretical vision about physics. This vision involves three loosely related parts.

- The fusion of real physic and various p-adic physics to a single coherent whole by generalizing the number concept by fusing real numbers and various p-adic number fields along common rationals. Extensions of p-adic number fields can be introduced by gluing them along common algebraic numbers to reals. Algebraic continuation of the physics from rationals and their their extensions to various number fields (generalization of completion process for rationals) is the key idea, and the challenge is to understand whether how one could achieve this dream. A profound implication is that purely local p-adic physics would code for the p-adic fractality of long length length scale real physics and vice versa, and one could understand the origins of p-adic length scale hypothesis.
- Second part of the vision involves
hyper counterparts of the classical number fields
defined as subspaces of their complexifications
with Minkowskian signature of metric. Allowed space-time surfaces
would correspond to what might be called
hyper-quaternionic sub-manifolds of a
hyper-octonionic space and mappable to M
^{4}× CP_{2}in natural manner. One could assign to each point of space-time surface a hyper-quaternionic 4-plane which is the plane defined by the modified gamma matrices but not tangent plane in general. Hence the basic variational principle of TGD would have deep number theoretic content. - The third part of the vision involves infinite
primes identifiable in terms of an
infinite hierarchy of second quantized arithmetic
quantum fields theories on one hand, and as having
representations as space-time surfaces analogous to
zero loci of polynomials on the other hand.
Single space-time point would have
an infinitely complex structure since real unity can
be represented as a ratio of infinite numbers in
infinitely many manners each having its own number
theoretic anatomy. Single space-time point would be
in principle able to represent in its structure
the quantum state of the entire universe. This
number theoretic variant of Brahman=Atman identity
would make Universe an algebraic hologram.
Number theoretical vision suggests that infinite hyper-octonionic or -quaternionic primes could could correspond directly to the quantum numbers of elementary particles and a detailed proposal for this correspondence is made. Furthermore, the generalized eigenvalue spectrum of the Chern-Simons Dirac operator could be expressed in terms of hyper-complex primes in turn defining basic building bricks of infinite hyper-complex primes from which hyper-octonionic primes are obtained by dicrete SU(3) rotations performed for finite hyper-complex primes.

Besides this holy trinity I will discuss loosely related topics. Included are possible applications of category theory in TGD framework; TGD inspired considerations related to Riemann hypothesis; topological quantum computation in TGD Universe; and TGD inspired approach to Langlands program.

**Category:** Mathematical Physics

[8] **viXra:1006.0037 [pdf]**
*replaced on 2012-01-30 21:56:36*

**Authors:** Matti Pitkänen

**Comments:** 28 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields discussed in this article, and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory.
In this article the connection between standard model symmetries and classical number fields
is discussed. The basis vision is that the geometry of the infinite-dimensional WCW ("world of
classical worlds") is unique from its mere existence. This leads to its identification as union of
symmetric spaces whose Kähler geometries are fixed by generalized conformal symmetries. This
fixes space-time dimension and the decomposition M^{4} x S and the idea is that the symmetries
of the Kähler manifold S make it somehow unique. The motivating observations are that the
dimensions of classical number fields are the dimensions of partonic 2-surfaces, space-time surfaces,
and imbedding space and M^{8} can be identified as hyper-octonions- a sub-space of complexified
octonions obtained by adding a commuting imaginary unit. This stimulates some questions.
Could one understand S = CP_{2} number theoretically in the sense that M^{8} and H = M^{4} x CP_{2}
be in some deep sense equivalent ("number theoretical compactification" or M^{8} - H duality)?
Could associativity define the fundamental dynamical principle so that space-time surfaces could
be regarded as associative or co-associative (defined properly) sub-manifolds of M^{8} or equivalently
of H.
One can indeed define the associativite (co-associative) 4-surfaces using octonionic representation
of gamma matrices of 8-D spaces as surfaces for which the modified gamma matrices span
an associate (co-associative) sub-space at each point of space-time surface. Also M^{8} - H duality
holds true if one assumes that this associative sub-space at each point contains preferred plane of
M^{8} identifiable as a preferred commutative or co-commutative plane (this condition generalizes
to an integral distribution of commutative planes in M^{8}). These planes are parametrized by CP_{2}
and this leads to M^{8} - H duality.
WCW itself can be identified as the space of 4-D local sub-algebras of the local Clifford
algebra of M^{8} or H which are associative or co-associative. An open conjecture is that this
characterization of the space-time surfaces is equivalent with the preferred extremal property of
Kähler action with preferred extremal identified as a critical extremal allowing infinite-dimensional
algebra of vanishing second variations.

**Category:** Mathematical Physics

[7] **viXra:1006.0036 [pdf]**
*replaced on 2012-01-30 21:58:07*

**Authors:** Matti Pitkänen

**Comments:** 51 Pages.

Physics as a generalized number theory program involves three threads: various p-adic physics
and their fusion together with real number based physics to a larger structure, the attempt to
understand basic physics in terms of classical number fields (in particular, identifying associativity
condition as the basic dynamical principle), and infinite primes whose construction is formally
analogous to a repeated second quantization of an arithmetic quantum field theory. In this article
p-adic physics and the technical problems relates to the fusion of p-adic physics and real physics
to a larger structure are discussed.
The basic technical problems relate to the notion of definite integral both at space-time level,
imbedding space level and the level of WCW (the "world of classical worlds"). The expressibility
of WCW as a union of symmetric spacesleads to a proposal that harmonic analysis of symmetric
spaces can be used to define various integrals as sums over Fourier components. This leads to the
proposal the p-adic variant of symmetric space is obtained by a algebraic continuation through a
common intersection of these spaces, which basically reduces to an algebraic variant of coset space
involving algebraic extension of rationals by roots of unity. This brings in the notion of angle
measurement resolution coming as Δφ = 2π/p^{n} for given p-adic prime p. Also a proposal how
one can complete the discrete version of symmetric space to a continuous p-adic versions emerges
and means that each point is effectively replaced with the p-adic variant of the symmetric space
identifiable as a p-adic counterpart of the real discretization volume so that a fractal p-adic variant
of symmetric space results.
If the Kähler geometry of WCW is expressible in terms of rational or algebraic functions, it
can in principle be continued the p-adic context. One can however consider the possibility that
that the integrals over partonic 2-surfaces defining
ux Hamiltonians exist p-adically as Riemann
sums. This requires that the geometries of the partonic 2-surfaces effectively reduce to finite
sub-manifold geometries in the discretized version of δM_{+}^{4}. If Kähler action is required
to exist p-adically same kind of condition applies to the space-time surfaces themselves. These
strong conditions might make sense in the intersection of the real and p-adic worlds assumed to
characterized living matter.

**Category:** Mathematical Physics

[6] **viXra:1006.0035 [pdf]**
*replaced on 2012-01-30 22:01:55*

**Authors:** Matti Pitkänen

**Comments:** 95 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first approach relies on a direct guess of Kähler function. Second
approach relies on the construction of Kähler form and metric utilizing the huge symmetries
of the geometry needed to guarantee the mathematical existence of Riemann connection. The
third approach discussed in this article relies on the construction of spinor structure based on the
hypothesis that complexified WCW gamma matrices are representable as linear combinations of
fermionic oscillator operator for the second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of spinor structure. This implies a
geometrization of fermionic statistics.
The basic philosophy is that at fundamental level the construction of WCW geometry reduces
to the second quantization of the induced spinor fields using Dirac action. This assumption
is parallel with the bosonic emergence stating that all gauge bosons are pairs of fermion and
antifermion at opposite throats of wormhole contact. Vacuum function is identified as Dirac
determinant and the conjecture is that it reduces to the exponent of Kähler function. In order
to achieve internal consistency induced gamma matrices appearing in Dirac operator must be
replaced by the modified gamma matrices defined uniquely by Kähler action and one must also
assume that extremals of Kähler action are in question so that the classical space-time dynamics
reduces to a consistency condition. This implies also super-symmetries and the fermionic oscillator
algebra at partonic 2-surfaces has intepretation as N = 1 generalization of space-time supersymmetry
algebra different however from standard SUSY algebra in that Majorana spinors are
not needed. This algebra serves as a building brick of various super-conformal algebras involved.
The requirement that there exist deformations giving rise to conserved Noether charges requires
that the preferred extremals are critical in the sense that the second variation of the Kähler action
vanishes for these deformations. Thus Bohr orbit property could correspond to criticality or at
least involve it.
Quantum classical correspondence demands that quantum numbers are coded to the properties
of the preferred extremals given by the Dirac determinant and this requires a linear coupling
to the conserved quantum charges in Cartan algebra. Effective 2-dimensionality allows a measurement
interaction term only in 3-D Chern-Simons Dirac action assignable to the wormhole
throats and the ends of the space-time surfaces at the boundaries of CD. This allows also to
have physical propagators reducing to Dirac propagator not possible without the measurement
interaction term. An essential point is that the measurement interaction corresponds formally
to a gauge transformation for the induced Kähler gauge potential. If one accepts the weak form
of electric-magnetic duality Kähler function reduces to a generalized Chern-Simons term and the
effect of measurement interaction term to Kähler function reduces effectively to the same gauge
transformation.
The basic vision is that WCW gamma matrices are expressible as super-symplectic charges at
the boundaries of CD. The basic building brick of WCW is the product of infinite-D symmetric
spaces assignable to the ends of the propagator line of the generalized Feynman diagram. WCW
Kähler metric has in this case "kinetic" parts associated with the ends and "interaction" part
between the ends. General expressions for the super-counterparts of WCW
ux Hamiltoniansand
for the matrix elements of WCW metric in terms of their anticommutators are proposed on basis
of this picture.

**Category:** Mathematical Physics

[5] **viXra:1006.0034 [pdf]**
*replaced on 2012-01-30 22:03:21*

**Authors:** Matti Pitkänen

**Comments:** 26 Pages.

There are three separate approaches to the challenge of constructing WCW Kähler geometry
and spinor structure. The first one relies on a direct guess of Kähler function. Second approach
relies on the construction of Kähler form and metric utilizing the huge symmetries of the geometry
needed to guarantee the mathematical existence of Riemann connection. The third approach relies
on the construction of spinor structure assuming that complexified WCW gamma matrices are
representable as linear combinations of fermionic oscillator operator for the second quantized free
spinor fields at space-time surface and on the geometrization of super-conformal symmetries in
terms of spinor structure.
In this article the construction of Kähler form and metric based on symmetries is discussed.
The basic vision is that WCW can be regarded as the space of generalized Feynman diagrams with
lines thickned to light-like 3-surfaces and vertices identified as partonic 2-surfaces. In zero energy
ontology the strong form of General Coordinate Invariance (GCI) implies effective 2-dimensionality
and the basic objects are pairs partonic 2-surfaces X^{2} at opposite light-like boundaries of causal
diamonds (CDs).
The hypothesis is that WCW can be regarded as a union of infinite-dimensional symmetric
spaces G/H labeled by zero modes having an interpretation as classical, non-quantum
uctuating
variables. A crucial role is played by the metric 2-dimensionality of the light-cone boundary
δM_{+}^{4}
+ and of light-like 3-surfaces implying a generalization of conformal invariance. The group
G acting as isometries of WCW is tentatively identified as the symplectic group of
δM_{+}^{4} x CP_{2}
localized with respect to X^{2}. H is identified as Kac-Moody type group associated with isometries
of H = M_{+}^{4} x CP_{2} acting on light-like 3-surfaces and thus on X^{2}.
An explicit construction for the Hamiltonians of WCW isometry algebra as so called
ux
Hamiltonians is proposed and also the elements of Kähler form can be constructed in terms of
these. Explicit expressions for WCW
ux Hamiltonians as functionals of complex coordinates of
the Cartesisian product of the infinite-dimensional symmetric spaces having as points the partonic
2-surfaces defining the ends of the the light 3-surface (line of generalized Feynman diagram) are
proposed.

**Category:** Mathematical Physics

[4] **viXra:1006.0033 [pdf]**
*replaced on 2012-01-30 22:05:03*

**Authors:** Matti Pitkänen

**Comments:** 29 Pages.

There are two basic approaches to quantum TGD. The first approach, which is discussed in
this article, is a generalization of Einstein's geometrization program of physics to an infinitedimensional
context. Second approach is based on the identification of physics as a generalized
number theory. The first approach relies on the vision of quantum physics as infinite-dimensional
Kähler geometry for the "world of classical worlds" (WCW) identified as the space of 3-surfaces
in in certain 8-dimensional space. There are three separate approaches to the challenge of constructing
WCW Kähler geometry and spinor structure. The first approach relies on direct guess
of Kähler function. Second approach relies on the construction of Kähler form and metric utilizing
the huge symmetries of the geometry needed to guarantee the mathematical existence of
Riemann connection. The third approach relies on the construction of spinor structure based on
the hypothesis that complexified WCW gamma matrices are representable as linear combinations
of fermionic oscillator operator for second quantized free spinor fields at space-time surface and
on the geometrization of super-conformal symmetries in terms of WCW spinor structure.
In this article the proposal for Kähler function based on the requirement of 4-dimensional General
Coordinate Invariance implying that its definition must assign to a given 3-surface a unique
space-time surface. Quantum classical correspondence requires that this surface is a preferred extremal
of some some general coordinate invariant action, and so called Kähler action is a unique
candidate in this respect. The preferred extremal has intepretation as an analog of Bohr orbit
so that classical physics becomes and exact part of WCW geometry and therefore also quantum
physics.
The basic challenge is the explicit identification of WCW Kähler function K. Two assumptions
lead to the identification of K as a sum of Chern-Simons type terms associated with the ends of
causal diamond and with the light-like wormhole throats at which the signature of the induced
metric changes. The first assumption is the weak form of electric magnetic duality. Second
assumption is that the Kähler current for preferred extremals satisfies the condition jK ^ djK = 0
implying that the
ow parameter of the
ow lines of jK defines a global space-time coordinate.
This would mean that the vision about reduction to almost topological QFT would be realized.
Second challenge is the understanding of the space-time correlates of quantum criticality.
Electric-magnetic duality helps considerably here. The realization that the hierarchy of Planck
constant realized in terms of coverings of the imbedding space follows from basic quantum TGD
leads to a further understanding. The extreme non-linearity of canonical momentum densities as
functions of time derivatives of the imbedding space coordinates implies that the correspondence
between these two variables is not 1-1 so that it is natural to introduce coverings of CD x CP_{2}.
This leads also to a precise geometric characterization of the criticality of the preferred extremals.

**Category:** Mathematical Physics

[3] **viXra:1006.0032 [pdf]**
*replaced on 2012-01-30 22:06:21*

**Authors:** Matti Pitkänen

**Comments:** 33 Pages.

There are two basic approaches to the construction of quantum TGD. The first approach
relies on the vision of quantum physics as infinite-dimensional Kähler geometry for the "world of
classical worlds" identified as the space of 3-surfaces in in certain 8-dimensional space. Essentially
a generalization of the Einstein's geometrization of physics program is in question. The second
vision is the identification of physics as a generalized number theory. This program involves
three threads: various p-adic physics and their fusion together with real number based physics
to a larger structure, the attempt to understand basic physics in terms of classical number fields
(in particular, identifying associativity condition as the basic dynamical principle), and infinite
primes whose construction is formally analogous to a repeated second quantization of an arithmetic
quantum field theory. In this article brief summaries of physics as infinite-dimensional geometry
and generalized number theory are given to be followed by more detailed articles.

**Category:** Mathematical Physics

[2] **viXra:1001.0042 [pdf]**
*replaced on 2012-03-11 09:16:42*

**Authors:** Jose Javier Garcia Moreta

**Comments:** 18 Pages.

ABSTRACT: In this paper we review some results of our previous papers involving Riemann
Hypothesis in the sense of Operator theory (Hilbert-Polya approach) and the application of the
negative values of the Zeta function (1 s) to the divergent integrals 1
0
s x dx
and to the
problem of defining a consistent product of distributions of the form ( ) ( ) m n D x D x , in this
paper we present new results of how the sums over the non-trivial zeros of the zeta function
h( )
can be related to the Mangoldt function 0 (x) assuming Riemann
Hypothesis.Throughout the paper we will use the notation ( ) ( ) R s s meaning that we use
the zeta regularization for the divergent series
0
s
n
n
s>0 or s=0

**Category:** Mathematical Physics

[1] **viXra:0907.0002 [pdf]**
*replaced on 10 Jul 2009*

**Authors:** Philip Gibbs

**Comments:** 5 pages

We prove that any 3x3 unitary matrix can be transformed to a magic matrix by multiplying its rows
and columns by phase factors. A magic matrix is defined as one for which the sum of the elements in any row
or column add to the same value. This result is relevant to recent observations on particle mixing matrices.

**Category:** Mathematical Physics