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Fuzzy Topology and Geometric Formalism of Quantum Mechanics

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Abstract

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.

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Authors and Affiliations

  1. Lebedev Institute of Physics, Leninsky pr., 53, Moscow, RU-117924, Russia

    S. Mayburov

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  1. S. Mayburov
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Mayburov, S. Fuzzy Topology and Geometric Formalism of Quantum Mechanics. Int J Theor Phys 54, 4272–4282 (2015). https://doi.org/10.1007/s10773-014-2480-3

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  • DOI: https://doi.org/10.1007/s10773-014-2480-3

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