Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects

Chaichian, M.; Demichev, A.; Presnajder, P.; Sheikh-Jabbari, M. M.; Tureanu, A.

Quantum Theories on Noncommutative Spaces with Nontrivial Topology: Aharonov-Bohm and Casimir Effects

Authors

Chaichian, M.

Demichev, A.

Presnajder, P.

Sheikh-Jabbari, M. M.

Tureanu, A.

Description

After discussing the peculiarities of quantum systems on noncommutative (NC) spaces with non-trivial topology and the operator representation of the $\star$-product on them, we consider the Aharonov-Bohm and Casimir effects for such spaces. For the case of the Aharonov-Bohm effect, we have obtained an explicit expression for the shift of the phase, which is gauge invariant in the NC sense. The Casimir energy of a field theory on a NC cylinder is divergent, while it becomes finite on a torus, when the dimensionless parameter of noncommutativity is a rational number. The latter corresponds to a well-defined physical picture. Certain distinctions from other treatments based on a different way of taking the noncommutativity into account are also discussed.
Latex file, 23 pages no figures, v2: typos removed, the version to appear in NPB. Reort No: HIP-2001-01/TH; IC/2001/3