Abstract
We argue that principles of quantum theory inevitably imply that any fundamental physical theory can be based only on a finite mathematics. A version of a quantum theory based on a Galois field (GFQT) with a characteristic p is described. Since any Galois field is finite, there are no infinities in this theory and all operators are well defined. In a formal limit p->\infty GFQT reproduces the results of standard theory based on continuity. In GFQT the notion of particle-antiparticle and the conservation of such additive quantum numbers as the electric, baryon and lepton charges can be only approximate if de Sitter energies are much less than p.
Felix M Lev