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.

arXiv commentv2: 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

References in corpus (9)

• Relational Quantum Mechanics
• Leading hadronic contribution to the muon magnetic moment from lattice QCD
• The Sudbury Neutrino Observatory
• New physics implications of recent search for $K_L\to {\pi }^0\nu \bar{\nu }$ at KOTO
• Generations: Three Prints, in Colour
• Subgroups of Clifford algebras
• A group-theorist's perspective on symmetry groups in physics
• Potential applications of modular representation theory to quantum mechanics
• Finite symmetry groups in physics

Cited by in corpus (2)

• Finite symmetry groups in physics
• Possible uses of the binary icosahedral group in grand unified theories