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arXiv · hep-th/0201070

Quantum mechanics on noncommutative Riemann surfaces

Bogdan Morariu·Alexios P. Polychronakos
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Abstract

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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Bogdan Morariu, Alexios P. Polychronakos. 2002-05-01. Quantum mechanics on noncommutative Riemann surfaces. https://doi.org/10.1016/s0550-3213(02)00298-5

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