Fuzzy Phase Space Structure as Approach to Quantization

Abstract

Modification of nonrelativistic phase space structure based on fuzzy ordered sets (Fosets) structure investigated as a possible quantization 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 ${\sigma }_x$. It's shown that proposed Mechanics on fuzzy phase space manifold reproduces the main quantum effects, in particular the interference of quantum states.

21 page, Latex, Talk given at Quantum Foundations Conference, Vaxjo, Sweden, 2001, to appear in Proceddings