Existence of Antiparticles as an Indication of Finiteness of Nature

TL;DR

This paper suggests that in a quantum theory over Galois fields, the existence of antiparticles naturally implies that nature might be fundamentally finite, challenging the traditional reliance on complex numbers.

Contribution

It generalizes Dirac's antiparticle result within a Galois field framework, proposing that antiparticles indicate a finite field structure of nature.

Findings

Antiparticles emerge from irreducible representations without local equations.

Existence of antiparticles suggests nature is described by finite fields.

Supports finite field models as fundamental in quantum theory.

Abstract

It is shown that in a quantum theory over a Galois field, the famous Dirac's result about antiparticles is generalized such that a particle and its antiparticle are already combined at the level of irreducible representations of the symmetry algebra without assuming the existence of a local covariant equation. We argue that the very existence of antiparticles is a strong indication that nature is described by a finite field rather than by complex numbers.