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

2001/09/21 by T. H. Hansson, Hansson, T. H., A. Karlhede +1 · 3 citations
Physics and Astronomy · #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mesoscale and Nanoscale Physics (cond-mat.mes-hall) #Noncommutative and Quantum Gravity Theories #Particle physics theoretical and experimental studies

paper · pdf · doi:10.48550/arxiv.cond-mat/0109413

openalex publication_date 2001/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Jain states in a matrix theory of the quantum Hall effect
• Semiclassical droplet states in matrix quantum Hall effect
• Time dependent solitons of noncommutative Chern-Simons theory coupled to scalar fields

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