Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2001-01-30
Nucl.Phys.B611:383-402,2001
Physics
High Energy Physics
High Energy Physics - Theory
Latex file, 23 pages no figures, v2: typos removed, the version to appear in NPB. Reort No: HIP-2001-01/TH; IC/2001/3
Scientific paper
10.1016/S0550-3213(01)00348-0
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.
Chaichian Masud
Demichev Andrei
Prešnajder Peter
Sheikh-Jabbari Mohammad M.
Tureanu Anca
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