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Charges and Currents in the Noncommutative Chern-Simons Theory of the QHE

T. H. Hansson·A. Karlhede
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Abstract

We couple the noncommutative Chern-Simons theory describing the fractional quantum Hall effect to external magnetic and electric potentials, and derive expressions for charge and current densities. To lowest non-trivial order the density operator satisfies the commutator algebra characteristic of the lowest Landau level. We take this as a strong indication that the theory correctly describes point particles in a strong magnetic field. We also obtain the correct QH response to a constant electric field, and density modulations in response to a weak variable magnetic field.

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T. H. Hansson, A. Karlhede. 2001-11-09. Charges and Currents in the Noncommutative Chern-Simons Theory of the QHE. https://arxiv.org/abs/cond-mat/0109413

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