Oscillators in a (2+1)-dimensional noncommutative space

We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncommutative space where the noncommutativity is induced by the shift of the dynamical variables with generators of SL(2,ℝ)SL(2,R) in a unitary irreducible representation considered in Falomir et al. [Phys. Rev. D 8...

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Detalles Bibliográficos
Autor principal: Vega, Federico Gaspar
Formato: Articulo
Lenguaje:Inglés
Publicado: 2014
Materias:
Física
Noncommutative space
Oscillator
Levi decomposition
Acceso en línea:http://sedici.unlp.edu.ar/handle/10915/102109
https://ri.conicet.gov.ar/11336/23743
Aporte de:
SEDICI (UNLP) de Universidad Nacional de La Plata
id I19-R120-10915-102109
record_format dspace
institution Universidad Nacional de La Plata
institution_str I-19
repository_str R-120
collection SEDICI (UNLP)
language Inglés
topic Física
Noncommutative space
Oscillator
Levi decomposition
spellingShingle Física
Noncommutative space
Oscillator
Levi decomposition
Vega, Federico Gaspar
Oscillators in a (2+1)-dimensional noncommutative space
topic_facet Física
Noncommutative space
Oscillator
Levi decomposition
description We study the Harmonic and Dirac Oscillator problem extended to a three-dimensional noncommutative space where the noncommutativity is induced by the shift of the dynamical variables with generators of SL(2,ℝ)SL(2,R) in a unitary irreducible representation considered in Falomir et al. [Phys. Rev. D 86, 105035 (2012)]. This redefinition is interpreted in the framework of the Levi's decomposition of the deformed algebra satisfied by the noncommutative variables. The Hilbert space gets the structure of a direct product with the representation space as a factor, where there exist operators which realize the algebra of Lorentz transformations. The spectrum of these models are considered in perturbation theory, both for small and large noncommutativity parameters, finding no constraints between coordinates and momenta noncommutativity parameters. Since the representation space of the unitary irreducible representations SL(2,ℝ)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.
format Articulo
Articulo
author Vega, Federico Gaspar
author_facet Vega, Federico Gaspar
author_sort Vega, Federico Gaspar
title Oscillators in a (2+1)-dimensional noncommutative space
title_short Oscillators in a (2+1)-dimensional noncommutative space
title_full Oscillators in a (2+1)-dimensional noncommutative space
title_fullStr Oscillators in a (2+1)-dimensional noncommutative space
title_full_unstemmed Oscillators in a (2+1)-dimensional noncommutative space
title_sort oscillators in a (2+1)-dimensional noncommutative space
publishDate 2014
url http://sedici.unlp.edu.ar/handle/10915/102109
https://ri.conicet.gov.ar/11336/23743
work_keys_str_mv AT vegafedericogaspar oscillatorsina21dimensionalnoncommutativespace
bdutipo_str Repositorios
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