https://doi.org/10.1051/epjconf/201612605009
Fuzzy Geometry of Commutative Spaces and Quantum Dynamics
Lebedev Institute of Physics, Moscow, Leninski pr. 53
a e-mail: mayburov@sci.lebedev.ru
Published online: 4 November 2016
Fuzzy topology and geometry considered as the possible mathematical framework for novel quantum-mechanical formalism. In such formalism the states of massive particle m correspond to the elements of fuzzy manifold called fuzzy points. Due to the manifold weak topology, m space coordinate x acquires principal uncertainty σx and described by the positive, normalized density w(
, t) in 3-dimensional case. It’s shown that the evolution of m state on such 3-dimensional manifold corresponds to Shroedinger dynamics of massive quantum particle.
© The Authors, published by EDP Sciences, 2016
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