Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry - INSPIRE

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Anisotropic harmonic oscillator, non-commutative Landau problem and exotic Newton-Hooke symmetry

Pedro D. Alvarez
(
- Chile U., Santiago
)
,
Joaquim Gomis
(
- Barcelona U., ECM and
- CERN
)
,
Kiyoshi Kamimura
(
- Toho U.
)
,
Mikhail S. Plyushchay
(
- Chile U., Santiago
)

Nov, 2007

12 pages

Published in:

Phys.Lett.B 659 (2008) 906-912

e-Print:

0711.2644 [hep-th]

DOI:

10.1016/j.physletb.2007.12.016

Report number:

CERN-PH-TH-2007-220,
UB-ECM-PF-07-32,
TOHO-CP-0786

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Abstract: (Elsevier)

We investigate the planar anisotropic harmonic oscillator with explicit rotational symmetry as a particle model with non-commutative coordinates. It includes the exotic Newton–Hooke particle and the non-commutative Landau problem as special, isotropic and maximally anisotropic, cases. The system is described by the same ( 2+1 )-dimensional exotic Newton–Hooke symmetry as in the isotropic case, and develops three different phases depending on the values of the two central charges. The special cases of the exotic Newton–Hooke particle and non-commutative Landau problem are shown to be characterized by additional, so(3) or so(2,1) Lie symmetry, which reflects their peculiar spectral properties.

oscillator: harmonic
oscillator: anisotropy
Landau problem: noncommutative
symmetry: rotation
symmetry: chiral
dimension: 3

References(29)

Figures(0)

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