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dc.contributor.author
Vega, Federico Gaspar
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dc.date.available
2017-09-06T23:06:07Z
dc.date.issued
2014-03
dc.identifier.citation
Vega, Federico Gaspar; Oscillators in a (2+1)-dimensional noncommutative space; American Institute of Physics; Journal of Mathematical Physics; 55; 3; 3-2014; 1-7
dc.identifier.issn
0022-2488
dc.identifier.uri
http://hdl.handle.net/11336/23743
dc.description.abstract
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.
dc.format
application/pdf
dc.language.iso
eng
dc.publisher
American Institute of Physics
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dc.rights
info:eu-repo/semantics/openAccess
dc.rights.uri
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.subject
Noncommutative Space
dc.subject
Oscillator
dc.subject
Levi Decomposition
dc.subject.classification
Otras Ciencias Físicas
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dc.subject.classification
Ciencias Físicas
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dc.subject.classification
CIENCIAS NATURALES Y EXACTAS
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dc.title
Oscillators in a (2+1)-dimensional noncommutative space
dc.type
info:eu-repo/semantics/article
dc.type
info:ar-repo/semantics/artículo
dc.type
info:eu-repo/semantics/publishedVersion
dc.date.updated
2017-09-06T19:28:35Z
dc.journal.volume
55
dc.journal.number
3
dc.journal.pagination
1-7
dc.journal.pais
Estados Unidos
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dc.journal.ciudad
Maryland
dc.description.fil
Fil: Vega, Federico Gaspar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Departamento de Física; Argentina
dc.journal.title
Journal of Mathematical Physics
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dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/doi/http://dx.doi.org/10.1063/1.4866914
dc.relation.alternativeid
info:eu-repo/semantics/altIdentifier/url/http://aip.scitation.org/doi/full/10.1063/1.4866914
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