2010/07/28 by Felix M. Lev, Lev, Felix M.
Physics and Astronomy · #FOS: Physical sciences #General Physics (physics.gen-ph) #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.1007.4875
9 pages, Latex. Motivation revisited and considerably shortened. arXiv admin note: substantial text overlap with arXiv:hep-th/0209001
arxiv created 2014/10/08 · arxiv updated 2014/10/09
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.