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Physics of Particles and Nuclei Letters

Fuzzy topology and geometric quantum formalism

Sergey Nikolaevich Mayburov

Published Dec 1, 2014• 3 citations
Publisher

Abstract

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of geometric quantum formalism. In such formalism the states of massive particle m correspond to elements of fuzzy manifold called fuzzy points. Due to their weak (partial) ordering, m space coordinate x acquires principal uncertainty σ x . It’s shown that m evolution with minimal number of additional assumptions obeys to schroedinger and dirac formalisms in norelativistic and relativistic cases correspondingly. It’s argued that particle’s interactions on such fuzzy manifold should be gauge invariant.

DOI
10.1134/s1547477114070322

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