The non-commutative Landau problem

Details The non-commutative Landau problem The non-commutative Landau problem

2002-01-02

arxiv.org/abs/hep-th/0201007v4

Ann.Phys.299:128-140,2002

Physics

High Energy Physics

High Energy Physics - Theory

Published with shortened title as Ann. Phys. (N. Y.) 299, pp. 128-140 (2002) 14 pages, LaTex, no figures

Scientific paper

10.1006/aphy.2002.6271

The Landau problem is discussed in two similar but still different non-commutative frameworks. The ``standard'' one, where the coupling to the gauge field is achieved using Poisson brackets, yields all Landau levels. The ``exotic'' approach, where the coupling to the gauge field is achieved using the symplectic structure, only yields lowest-Landau level states, as advocated by Peierls and used in the description of the ground states of the Fractional Quantum Hall Effect. The same reduced model also describes vortex dynamics in a superfluid ${}^4$He film. Remarkably, the spectrum depends crucially on the quantization scheme. The system is symmetric w. r. t. area-preserving diffeomorphisms.

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