Massless Elementary Particles in a Quantum Theory Over a Galois Field

TL;DR

This paper explores a quantum theory over Galois fields, revealing a new particle-antiparticle symmetry that restricts massless elementary particles to half-integer spins and suggests photons and gravitons are composite.

Contribution

It demonstrates the compatibility of a novel symmetry with operators for massless particles in GFQT and derives implications for particle spin and composition.

Findings

Massless particles in GFQT have only half-integer spins.

Neutral massless elementary particles cannot exist in GFQT.

Photons and gravitons are likely composite in GFQT.

Abstract

We consider massless elementary particles in a quantum theory based on a Galois field (GFQT). We previously showed that the theory has a new symmetry between particles and antiparticles, which has no analogue in the standard approach. We now prove that the symmetry is compatible with all operators describing massless particles. Consequently, massless elementary particles can have only the half-integer spin (in conventional units), and the existence of massless neutral elementary particles is incompatible with the spin-statistics theorem. In particular, this implies that the photon and the graviton in the GFQT can only be composite particles.