Fuzzy Topology and Geometric Formalism of Quantum Mechanics

Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric 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 principa...

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Bibliographic Details
Published inInternational journal of theoretical physics Vol. 54; no. 12; pp. 4272 - 4282
Main Author Mayburov, S.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.12.2015
Subjects
Elementary Particles
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Theoretical
Quantization
Fuzzy topology
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Summary:Dodson-Zeeman fuzzy topology considered as the possible mathematical framework of quantum geometric 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 on such manifold corresponds to quantum dynamics. It’s argued also that particle’s interactions on such fuzzy manifold should be gauge invariant.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-014-2480-3