Quantum mechanics on noncommutative Riemann surfaces

Details Quantum mechanics on noncommutative Riemann surfaces Quantum mechanics on noncommutative Riemann surfaces

2002-01-11

arxiv.org/abs/hep-th/0201070v2

Nucl.Phys. B634 (2002) 326-338

Physics

High Energy Physics

High Energy Physics - Theory

18 pages, 1 figure, final version to appear in Nucl.Phys.B

Scientific paper

10.1016/S0550-3213(02)00298-5

We study the quantum mechanics of a charged particle on a constant curvature noncommutative Riemann surface in the presence of a constant magnetic field. We formulate the problem by considering quantum mechanics on the noncommutative AdS_2 covering space and gauging a discrete symmetry group which defines a genus-g surface. Although there is no magnetic field quantization on the covering space, a quantization condition is required in order to have single-valued states on the Riemann surface. For noncommutative AdS_2 and subcritical values of the magnetic field the spectrum has a discrete Landau level part as well as a continuum, while for overcritical values we obtain a purely noncommutative phase consisting entirely of Landau levels.

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