This article is cited in 1 paper

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.

Received: 03.09.1992

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

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