(2 + 1)D exotic Newton–Hooke symmetry, duality and projective phase

A particle system with a (2 + 1)D exotic Newton–Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic os...

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Bibliographic Details
Published in:Annals of physics 2007-07, Vol.322 (7), p.1556-1586
Main Authors: Alvarez, Pedro D., Gomis, Joaquim, Kamimura, Kiyoshi, Plyushchay, Mikhail S.
Format: Article
Language:English
Subjects:
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
COMMUTATION RELATIONS
DUALITY
Exotic Newton–Hooke symmetry
Mathematics
Noncommutative plane
NONLINEAR PROBLEMS
Nonlinear realization
Nonlinear systems
OSCILLATORS
Particle physics
Projective phase
SYMMETRY
THREE-DIMENSIONAL CALCULATIONS
TRANSFORMATIONS
WAVE EQUATIONS
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Summary:A particle system with a (2 + 1)D exotic Newton–Hooke symmetry is constructed by the method of nonlinear realization. It has three essentially different phases depending on the values of the two central charges. The subcritical and supercritical phases (describing 2D isotropic ordinary and exotic oscillators) are separated by the critical phase (one-mode oscillator), and are related by a duality transformation. In the flat limit, the system transforms into a free Galilean exotic particle on the noncommutative plane. The wave equations carrying projective representations of the exotic Newton–Hooke symmetry are constructed.
ISSN:0003-4916
1096-035X
DOI:10.1016/j.aop.2007.03.002