Fuzzy Geometry of Phase Space and Quantization of Massive Fields

TL;DR

This paper explores a fuzzy geometric approach to phase space and quantization, deriving quantum mechanics formalism from fuzzy structures with minimal assumptions.

Contribution

It introduces a fuzzy phase space framework using Foset structures, providing a new foundation for deriving quantum mechanics.

Findings

Quantum space-time modeled as fuzzy phase space.

Derivation of Schrödinger formalism from fuzzy geometry.

Uncertainty in position arises naturally from fuzzy ordering.

Abstract

The quantum space-time and the phase space with fuzzy structure is investigated as the possible quantization formalism. In this theory the state of nonrelativistic particle corresponds to the element of fuzzy ordered set (Foset) - fuzzy point. Due to Foset partial (weak) ordering, particle's space coordinate x acquires principal uncertainty dx. It's shown that Shroedinger formalism of Quantum Mechanics can be completely derived from consideration of particle evolution in fuzzy phase space with minimal number of axioms.