Geodesic
Weyl correspondence for a charged particle in the field of a magnetic monopole
Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 383-398 Cet article a éte moissonné depuis la source Math-Net.Ru

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We construct a generalized Weyl correspondence for an electrically charged particle in the field of the Dirac magnetic monopole. Our starting points are a global Lagrangian description of this system as a constrained system with $U(1)$ gauge symmetry given in terms of the fiber bundle theory and a reduction of the presymplectic structure arising on the constraint surface. In contrast to the recently proposed quantization scheme based on using a quaternionic Hilbert module, the quantum operators corresponding to classical observables in our construction act in the complex Hilbert space of $U(1)$-equivariant functions introduced by Greub and Petry. These functions are defined on the total space of a fiber bundle that is topologically equivalent to the Hopf fibration.
Keywords: Weyl correspondence, star product, magnetic monopole, Hopf fibration, gauge symmetry, presymplectic reduction.
Mots-clés : charge quantization 
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M. A. Soloviev. Weyl correspondence for a charged particle in the field of a magnetic monopole. Teoretičeskaâ i matematičeskaâ fizika, Tome 187 (2016) no. 2, pp. 383-398. http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a11/

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