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

Voir la notice de l'article provenant de la source Math-Net.Ru

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 
@article{TMF_2016_187_2_a11,
     author = {M. A. Soloviev},
     title = {Weyl correspondence for a~charged particle in the~field of a~magnetic monopole},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {383--398},
     publisher = {mathdoc},
     volume = {187},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a11/}
}
TY  - JOUR
AU  - M. A. Soloviev
TI  - Weyl correspondence for a~charged particle in the~field of a~magnetic monopole
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2016
SP  - 383
EP  - 398
VL  - 187
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a11/
LA  - ru
ID  - TMF_2016_187_2_a11
ER  - 
%0 Journal Article
%A M. A. Soloviev
%T Weyl correspondence for a~charged particle in the~field of a~magnetic monopole
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2016
%P 383-398
%V 187
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TMF_2016_187_2_a11/
%G ru
%F TMF_2016_187_2_a11
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/