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Journal of Physics Conference Series

Commutative Fuzzy Geometry and Geometric Quantum Mechanics

Sergey Nikolaevich Mayburov

Published Jul 1, 2018• 4 citations
Publisher

Abstract

Commutative fuzzy geometry considered as the possible mathematical framework for reformulation of quantum-mechanical formalism in strictly geometric terms. In that approach the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to manifold weak topology, in 1-dimensional case m space coordinate x acquires principal uncertainty σ x and described by positive, normalized density ω ( x,t ), the analogous uncertainties appear for 3-dimensional manifold. It's shown that m states on such manifold are equivalent to Dirac vectors of complex Hilbert space, their evolution correspond to Shroedinger dynamics of massive quantum particle.

DOI
10.1088/1742-6596/1051/1/012022

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