Quantum mechanics and quantum Hall effect on Riemann surfaces

Details Quantum mechanics and quantum Hall effect on Riemann surfaces Quantum mechanics and quantum Hall effect on Riemann surfaces

1993-07-02

arxiv.org/abs/hep-th/9307011v1

Nucl.Phys. B413 (1994) 735-753

Physics

High Energy Physics

High Energy Physics - Theory

24 pages, Latex

Scientific paper

10.1016/0550-3213(94)90010-8

The quantum mechanics of a system of charged particles interacting with a magnetic field on Riemann surfaces is studied. We explicitly construct the wave functions of ground states in the case of a metric proportional to the Chern form of the $\theta$-bundle, and the wave functions of the Landau levels in the case of the the Poincar{\' e} metric. The degeneracy of the the Landau levels is obtained by using the Riemann-Roch theorem. Then we construct the Laughlin wave function on Riemann surfaces and discuss the mathematical structure hidden in the Laughlin wave function. Moreover the degeneracy of the Laughlin states is also discussed.

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