Fuzzy Topology, Quantization and Gauge Invariance
arXiv:1205.3019 · doi:10.1134/S1063779612050267
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 dx. 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.
12 pages, Talk given on 'Geometry and Field Theory' conference, Porto, July 2012. To be published in Int. J. Theor. Phys. (2015)