  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.
