Fuzzy Phase Space Structure as Approach to Quantization

TL;DR

This paper proposes a novel quantization framework using fuzzy ordered sets in phase space, which reproduces key quantum effects like interference through fuzzy points and inherent uncertainties.

Contribution

It introduces a fuzzy phase space structure based on Fosets as a new approach to quantization, linking fuzzy ordering to quantum phenomena.

Findings

Reproduces quantum interference effects

Introduces inherent uncertainty in position due to fuzzy ordering

Provides a new geometric framework for quantum mechanics

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.