Geodesic
Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge
Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 44-63 
O. M. Ivanov; A. G. Savinkov. Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge. Teoretičeskaâ i matematičeskaâ fizika, Tome 96 (1993) no. 1, pp. 44-63. http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a3/
@article{TMF_1993_96_1_a3,
     author = {O. M. Ivanov and A. G. Savinkov},
     title = {Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {44--63},
     year = {1993},
     volume = {96},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_1993_96_1_a3/}
}
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The quantum mechanics of a system of particles on $S^1$ is considered. We describe the main properties of the dynamics of manyparticle configurations defined on global spaces of $U(1)$ bundles, which are realized as dynamical spaces on the quantization of systems possessing singularities (globally non-Hamiltonian on the original domain of definitionS $S^1 \times \cdots \times S^1$. The absence of an operation of particle permutation compatible with the structure of the fiber bundle is noted. It reveals a similarity between these systems and anyons.

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