Authors: Wayne R. Lundberg
The No-Boundary Wave Function (NBWF) instanton formulation provides a particle theory basis due to its consistency with causality and cosmology. Terms of the NBWF instanton action are identified with intrinsic metrics of finite-dimensional particle theory. This approach yields a new type of finitary particle theory, in which the string (or finite graviton) is replaced with band representation geometry. A band is simply the well-known string with an intrinsic stiffness. Representation geometric metrics of area and curvature are thus intrinsic descriptors of particle mass and energy. The ground states of a band are inherently tripartite (having three portions), which motivates assignment of QCD color local gauge fields to portions of the band. For completeness, band-theoretic representation requires a quantum state algebra. A quantum state algebra that is one-to-one with standard model particle theory was sought -and found. The band theory quantum state algebra is a subgroup of index 12 of a cross product of two wreath products. A subgroup of this unique non-commutative algebra has proven to be 1-1 with standard model QCD particles, via its fundamental tie to preons. Further, band theory produces exactly three particle generations (or families or flavors). Three flavors of neutrinos are thus predicted by a well-founded particle formulation, which is qualitatively consistent with observations of massive oscillating neutrinos. Band theory is the particulate portion of a comprehensive theory, which includes cyclic cosmology. Cyclic cosmology has been demonstrated to have no cosmological coincidence problem.
Comments: 7 Pages. 5 figures, Presentation at the DPF 2015 Meeting of the American Physical Society Division of Particles and Fields, Ann Arbor, Michigan, August 4-8, 2015.
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