Quantum Mechanics on the Noncommutative Torus

Details Quantum Mechanics on the Noncommutative Torus Quantum Mechanics on the Noncommutative Torus

2001-02-22

arxiv.org/abs/hep-th/0102157v4

Nucl.Phys. B610 (2001) 531-544

Physics

High Energy Physics

High Energy Physics - Theory

LaTeX, 19 pages, no figures, references added

Scientific paper

10.1016/S0550-3213(01)00294-2

We analyze the algebra of observables of a charged particle on a noncommutative torus in a constant magnetic field. We present a set of generators of this algebra which coincide with the generators for a commutative torus but at a different value of the magnetic field, and demonstrate the existence of a critical value of the magnetic field for which the algebra reduces. We then obtain the irreducible representations of the algebra and relate them to noncommutative bundles. Finally we comment on Landau levels, density of states and the critical case.

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