  We consider a quantum theory based on a Galois field. In this approach
infinities cannot exist, the cosmological constant problem does not arise, and
one irreducible representation (IR) of the symmetry algebra splits into
independent IRs describing a particle an its antiparticle only in the
approximation when de Sitter energies are much less than the characteristic of
the field. As a consequence, the very notions of particles and antiparticles
are only approximate and such additive quantum numbers as the electric, baryon
and lepton charges are conserved only in this approximation. There can be no
neutral elementary particles and the spin-statistics theorem can be treated
simply as a requirement that standard quantum theory should be based on complex
numbers.
