Geodesic
Charge dynamics on $U(1)$ abundles
Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 36-50 Cet article a éte moissonné depuis la source Math-Net.Ru

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The quantum dynamics of a particle on $(2d-2)$ universal $U(1)$ fiber bundles is considered. The analysis on these bundles generalizes, in particular, the description of a system consisting of a charge and a Dirac magnetic monopole. The spectral properties of Hamiltonians of a charge in a connection field of monopole type are studied, and a representation in which they have a simple form is found. The complete set of states in the global spaces of the $U(1)$ bundles graded by the topological number $n$ is constructed. It is shown that in each sector of the state space corresponding to the number $n\ne0$ spatial parity is violated. The violation is topological in nature, i.e., it does not depend on the choice of the connection in the considered fiber bundles. 
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A. B. Ryzhov; A. G. Savinkov. Charge dynamics on $U(1)$ abundles. Teoretičeskaâ i matematičeskaâ fizika, Tome 91 (1992) no. 1, pp. 36-50. http://geodesic.mathdoc.fr/item/TMF_1992_91_1_a3/

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