Artículo
Noncommutativity in (2+1)-dimensions and the Lorentz group
Fecha de publicación:
11/2012
Editorial:
American Physical Society
Revista:
Physical Review D: Particles, Fields, Gravitation and Cosmology
ISSN:
0556-2821
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
In this article we considered models of particles living in a three-dimensional space-time with a nonstandard noncommutativity induced by shifting canonical coordinates and momenta with generators of a unitary irreducible representation of the Lorentz group. The Hilbert space gets the structure of a direct product with the representation space, where we are able to construct operators which realize the algebra of Lorentz transformations. We study the modified Landau problem for both Schrödinger and Dirac particles, whose Hamiltonians are obtained through a kind of non-Abelian Bopp's shift of the dynamical variables from the ones of the usual problem in the normal space. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters. We find no constraint between the parameters referring to noncommutativity in coordinates and momenta but they rather play similar roles. Since the representation space of the unitary irreducible representations SL(2,R) can be realized in terms of spaces of square-integrable functions, we conclude that these models are equivalent to quantum mechanical models of particles living in a space with an additional compact dimension. © 2012 American Physical Society.
Palabras clave:
Noncommutative Space
,
Lorentz Group
,
Quantum Mechanics Model
,
Landau Problem
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Articulos(IFLP)
Articulos de INST.DE FISICA LA PLATA
Articulos de INST.DE FISICA LA PLATA
Citación
Falomir, Horacio Alberto; Vega, Federico Gaspar; Gamboa, Jorge; Mendez, Fernando; Loewe, Marcelo ; Noncommutativity in (2+1)-dimensions and the Lorentz group; American Physical Society; Physical Review D: Particles, Fields, Gravitation and Cosmology; 86; 10; 11-2012
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