2 Fuzzy Phase Space Structure as Approach to Quantization

Modification of a nonrelativistic phase space structure based on fuzzy ordered sets (Fosets) structure investigated as a possible nonrelativistic quan-tization framework. In this model particle's m state corresponds to Foset element-fuzzy point. Due to fuzzy ordering its space coordinate x acquires principal uncertainty σ x. It's shown that proposed Mechanics on fuzzy phase space manifold reproduces the main quantum effects, in particular the interference of quantum states. 1 Introduction Quantum Mechanics (QM) is now a well established physical theory, yet its relation with physical space-time structure and relativity isn't quite clear and actively discussed now. This interest enforced by the recent indications that space-time properties at small (Planck) scale can be quite exotic [1, 2]. Due to the absence of any experimental information it seems instructive to look for some indications reconsidering under this angle standard Quantum Physics space-time picture. The additional attention to QM foundations induced also by Gravity quantization problems. In particular Isham proposed that some space-time properties like the metrics or topological structure, assumed in the standard quantization should be modified significantly or even rejected completely [5]. Our work motivated largely by this ideas in which framework we explore Set structure of space-time manifold M s−t. Remind that for