## Fibonacci Oscillators and (P, q)-Deformed Lorentz Transformations

**Authors:** Carlos Castro

The two-parameter quantum calculus used in the construction of Fibonacci oscillators is briefly reviewed before presenting the $ (p, q)$-deformed Lorentz transformations which leave invariant the Minkowski spacetime interval $ t^2 - x^2 - y^2 - z^2$. Such transformations require the introduction of three different types of exponential functions leading to the $(p, q)$-analogs of hyperbolic and trigonometric functions. The composition law of two successive Lorentz boosts (rotations) is $no$ longer additive $ \xi_3 \not= \xi_1 + \xi_2$ ( $ \theta_3 \not= \theta_1 + \theta_2$). We finalize with a discussion on quantum groups, noncommutative spacetimes, $\kappa$-deformed Poincare algebra and quasi-crystals.

**Comments:** 12 Pages.

**Download:** **PDF**

### Submission history

[v1] 2018-07-01 21:29:24

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