Marcelo M. Amaral, Klee Irwin (2018)
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.
On the Poincaré Group at the 5th Root of Unity
Marcelo Amaral · Klee Irwin
Received: date / Accepted: date
Abstract Considering the predictions from the standard model of particle
physics coupled with experimental results from particle accelerators, we dis-
cuss a scenario in which from the infinite possibilities in the Lie groups we use
to describe particle physics, nature needs only the lower dimensional represen-
tations − 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 sym-
metry content of relativistic quantum fields in accordance with the well known
Wigner classification. Further connections of the 5th root of unity quantiza-
tion 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
1 Introduction
One of the key ideas of modern physics, which is present in the construction
of the standard model of particle physics, is the concept of a field, which is a
Marcelo Amaral
Quantum Gravity Research
Los Angeles, CA
E-mail: Marcelo@QuantumGravityResearch.org
Klee Irwin
Quantum Gravity Research
Los Angeles, CA
E-mail: Klee@QuantumGravityResearch.org
Preprints (www.preprints.org) | NOT PEER-REVIEWED | Posted: 13 March 2019
© 2019 by the author(s). Distributed under a Creative Commons CC BY license.
doi:10.20944/preprints201903.0137.v1
2
Marcelo Amaral, Klee Irwin
representation of a Lie group. In this framework of quantum field theory, spin
and mass arise via the representation theory of the Poincaré group. Charge
is associated with internal gauge symmetry, th