Preprint Article Version 2 Preserved in Portico This version is not peer-reviewed

On the Poincaré Group at the Fifth Root of Unity

Version 1 : Received: 11 March 2019 / Approved: 13 March 2019 / Online: 13 March 2019 (06:44:00 CET)
Version 2 : Received: 3 May 2019 / Approved: 6 May 2019 / Online: 6 May 2019 (09:06:55 CEST)

How to cite: Amaral, M.; Irwin, K. On the Poincaré Group at the Fifth Root of Unity. Preprints 2019, 2019030137. Amaral, M.; Irwin, K. On the Poincaré Group at the Fifth Root of Unity. Preprints 2019, 2019030137.


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 algebra at the fifth root of unity can be used to address the quantum Lorentz group representation theory through its universal covering 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 fifth 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.


quantum groups; quantum gravity; quantum information; particle physics; quasicrystals; Fibonacci anyons


Physical Sciences, Quantum Science and Technology

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