Fuzzy Topology and Geometric Formalism of Quantum Mechanics
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.
- Publication:
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International Journal of Theoretical Physics
- Pub Date:
- December 2015
- DOI:
- 10.1007/s10773-014-2480-3
- Bibcode:
- 2015IJTP...54.4272M
- Keywords:
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- Fuzzy topology;
- Quantization