Options for a finite group model of quantum mechanics
Abstract
There are four finite groups that could plausibly play the role of the spin group in a finite or discrete model of quantum mechanics, namely the four double covers of the three rotation groups of the Platonic solids. In an earlier paper I have considered in detail how the smallest of these groups, namely the binary tetrahedral group, of order 24, could give rise to a non-relativistic theory that contains much of the structure of the standard model of particle physics. In this paper I consider how one of the two double covers of the rotation group of the cube might extend this to a relativistic theory.
Keywords
Cite
@article{arxiv.2104.10165,
title = {Options for a finite group model of quantum mechanics},
author = {Robert A. Wilson},
journal= {arXiv preprint arXiv:2104.10165},
year = {2021}
}
Comments
v2: added a section showing how to obtain a modified Dirac algebra that is generally covariant, and discussed possible applications to a mass gauge and the muon g-2 anomaly. v3: added sections on chirality and neutrinos, and relationships to other models. v4: simplified notation, clarified arguments, added sections on the wave-function and quantisation. v5: 33 pages