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The non-commutative oscillator, symmetry and the Landau problem

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Abstract

The isotropic oscillator on a plane is discussed where the coordinate and momentum space are both considered to be non-commutative. We also discuss the symmetry properties of the oscillator for three separate cases when the non-commutative parameters Θ and \(\overline{\Theta}\) for x and p-space, respectively, satisfy specific relations. We compare the Landau problem with the isotropic oscillator on non-commutative space and obtain a relation between the two non-commutative parameters and the magnetic field of the Landau problem.

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Authors and Affiliations

  1. Theory Division, Saha Institute of Nuclear Physics, 1/AF Bidhannagar, Calcutta, 700064, India

    Pulak Ranjan Giri

  2. Physics and Applied Mathematics Unit, Indian Statistical Institute, Calcutta, 700108, India

    P. Roy

Authors
  1. Pulak Ranjan Giri
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  2. P. Roy
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Correspondence to Pulak Ranjan Giri.

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Giri, P.R., Roy, P. The non-commutative oscillator, symmetry and the Landau problem. Eur. Phys. J. C 57, 835–839 (2008). https://doi.org/10.1140/epjc/s10052-008-0705-4

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  • DOI: https://doi.org/10.1140/epjc/s10052-008-0705-4

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