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TMF, 1993, Volume 96, Number 1, Pages 44–63 (Mi tmf1490)  

Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge

O. M. Ivanov, A. G. Savinkov

P. N. Lebedev Physical Institute, Russian Academy of Sciences

Abstract: 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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English version:
Theoretical and Mathematical Physics, 1993, 96:1, 806–817

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Received: 03.09.1992

Citation: O. M. Ivanov, A. G. Savinkov, “Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge”, TMF, 96:1 (1993), 44–63; Theoret. and Math. Phys., 96:1 (1993), 806–817

Citation in format AMSBIB
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\by O.~M.~Ivanov, A.~G.~Savinkov
\paper Nontrivial $U(1)$ bundles over tori and properties of many-particle systems with topological charge
\jour TMF
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\vol 96
\issue 1
\pages 44--63
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\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1243859}
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\transl
\jour Theoret. and Math. Phys.
\yr 1993
\vol 96
\issue 1
\pages 806--817
\crossref{https://doi.org/10.1007/BF01074109}
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  • Теоретическая и математическая физика Theoretical and Mathematical Physics
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