Noncommutativity in (2+1)-dimensions and the Lorentz group

Autores
Falomir, Horacio Alberto; Vega, Federico Gaspar; Gamboa, Jorge; Mendez, Fernando; Loewe, Marcelo
Año de publicación
2012
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
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.
Fil: Falomir, Horacio Alberto. 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
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
Fil: Gamboa, Jorge. Universidad de Santiago de Chile; Chile
Fil: Mendez, Fernando. Universidad de Santiago de Chile; Chile
Fil: Loewe, Marcelo. Centre For Theoretical Physics And Mathematical Physics; Chile
Materia
Noncommutative space
Lorentz Group
Quantum Mechanics Model
Landau Problem
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/74566
Acceder
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oai_identifier_str oai:ri.conicet.gov.ar:11336/74566
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network_name_str CONICET Digital (CONICET)
spelling Noncommutativity in (2+1)-dimensions and the Lorentz groupFalomir, Horacio AlbertoVega, Federico GasparGamboa, JorgeMendez, FernandoLoewe, MarceloNoncommutative spaceLorentz GroupQuantum Mechanics ModelLandau Problemhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1In 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.Fil: Falomir, Horacio Alberto. 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; ArgentinaFil: 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; ArgentinaFil: Gamboa, Jorge. Universidad de Santiago de Chile; ChileFil: Mendez, Fernando. Universidad de Santiago de Chile; ChileFil: Loewe, Marcelo. Centre For Theoretical Physics And Mathematical Physics; ChileAmerican Physical Society2012-11info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/74566Falomir, 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; 11-20120556-2821CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.86.105035info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.105035info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-29T10:21:42Zoai:ri.conicet.gov.ar:11336/74566instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-29 10:21:43.074CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Noncommutativity in (2+1)-dimensions and the Lorentz group
title Noncommutativity in (2+1)-dimensions and the Lorentz group
spellingShingle Noncommutativity in (2+1)-dimensions and the Lorentz group
Falomir, Horacio Alberto
Noncommutative space
Lorentz Group
Quantum Mechanics Model
Landau Problem
title_short Noncommutativity in (2+1)-dimensions and the Lorentz group
title_full Noncommutativity in (2+1)-dimensions and the Lorentz group
title_fullStr Noncommutativity in (2+1)-dimensions and the Lorentz group
title_full_unstemmed Noncommutativity in (2+1)-dimensions and the Lorentz group
title_sort Noncommutativity in (2+1)-dimensions and the Lorentz group
dc.creator.none.fl_str_mv Falomir, Horacio Alberto
Vega, Federico Gaspar
Gamboa, Jorge
Mendez, Fernando
Loewe, Marcelo
author Falomir, Horacio Alberto
author_facet Falomir, Horacio Alberto
Vega, Federico Gaspar
Gamboa, Jorge
Mendez, Fernando
Loewe, Marcelo
author_role author
author2 Vega, Federico Gaspar
Gamboa, Jorge
Mendez, Fernando
Loewe, Marcelo
author2_role author
author
author
author
dc.subject.none.fl_str_mv Noncommutative space
Lorentz Group
Quantum Mechanics Model
Landau Problem
topic Noncommutative space
Lorentz Group
Quantum Mechanics Model
Landau Problem
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv 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.
Fil: Falomir, Horacio Alberto. 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
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
Fil: Gamboa, Jorge. Universidad de Santiago de Chile; Chile
Fil: Mendez, Fernando. Universidad de Santiago de Chile; Chile
Fil: Loewe, Marcelo. Centre For Theoretical Physics And Mathematical Physics; Chile
description 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.
publishDate 2012
dc.date.none.fl_str_mv 2012-11
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/74566
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
0556-2821
CONICET Digital
CONICET
url http://hdl.handle.net/11336/74566
identifier_str_mv 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
0556-2821
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevD.86.105035
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/prd/abstract/10.1103/PhysRevD.86.105035
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.070432

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