Fuzzy geometry of phase space and quantization of massive fields

The quantum spacetime and the phase space with fuzzy structure are investigated as the possible quantization formalism. In this theory, the state of the nonrelativistic particle m corresponds to the element of fuzzy ordered set (Foset), i.e. the fuzzy point. Due to Foset partial ( weak) ordering, the m space coordinate x acquires principal uncertainty sigma(x). It is shown that Schrodinger formalism of quantum mechanics can be completely derived from consideration of m evolution in fuzzy phase space with minimal number of axioms.