Preprint
Article

On the Poincaré Group at the 5th Root of Unity

This version is not peer-reviewed.

Submitted:

11 March 2019

Posted:

13 March 2019

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Abstract
Considering the predictions from the standard model of particle physics coupled with experimental results from particle accelerators, we discuss a scenario in which from the infinite possibilities in the Lie groups we use to describe particle physics, nature needs only the lower dimensional representations − an important phenomenology that we argue indicates nature is code theoretic. We show that the “quantum” deformation of the SU (2) Lie group at the 5th root of unity can be used to address the quantum Lorentz group and gives the right low dimensional physical realistic spin quantum numbers confirmed by experiments. In this manner we can describe the spacetime symmetry content of relativistic quantum fields in accordance with the well known Wigner classification. Further connections of the 5th root of unity quantization with the mass quantum number associated with the Poincaré Group and the SU (N ) charge quantum numbers are discussed as well as their implication for quantum gravity.
Keywords: 
quantum groups; quantum gravity; quantum information; particle physics; quasicrystals; Fibonacci anyons
Subject: 
Physical Sciences  -   Quantum Science and Technology
Copyright: This open access article is published under a Creative Commons CC BY 4.0 license, which permit the free download, distribution, and reuse, provided that the author and preprint are cited in any reuse.

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