On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space

Autores
Falomir, Horacio Alberto; González Pisani, Pablo Andrés; Vega, Federico Gaspar; Cárcamo, D.; Méndez, F.; Loewe, M.
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras sl (2, ?) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
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: González Pisani, Pablo Andrés. 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: Cárcamo, D.. Universidad de Santiago de Chile; Chile
Fil: Méndez, F.. Universidad de Santiago de Chile; Chile
Fil: Loewe, M.. Pontificia Universidad Católica de Chile; Chile
Materia
NONCOMMUTATIVE PHASE SPACE
QUANTUM MECHANICS
SPECTRUM OF ROTATIONALLY INVARIANT HAMILTONIANS
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:11336/54415
Acceder
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spelling On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase spaceFalomir, Horacio AlbertoGonzález Pisani, Pablo AndrésVega, Federico GasparCárcamo, D.Méndez, F.Loewe, M.NONCOMMUTATIVE PHASE SPACEQUANTUM MECHANICSSPECTRUM OF ROTATIONALLY INVARIANT HAMILTONIANShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras sl (2, ?) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.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: González Pisani, Pablo Andrés. 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: Cárcamo, D.. Universidad de Santiago de Chile; ChileFil: Méndez, F.. Universidad de Santiago de Chile; ChileFil: Loewe, M.. Pontificia Universidad Católica de Chile; ChileIOP Publishing2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/54415Falomir, Horacio Alberto; González Pisani, Pablo Andrés; Vega, Federico Gaspar; Cárcamo, D.; Méndez, F.; et al.; On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 49; 1; 1-2016; 55202-552481751-8113CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/5/055202info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-10-15T14:27:27Zoai:ri.conicet.gov.ar:11336/54415instacron: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:34982025-10-15 14:27:27.803CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
spellingShingle On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
Falomir, Horacio Alberto
NONCOMMUTATIVE PHASE SPACE
QUANTUM MECHANICS
SPECTRUM OF ROTATIONALLY INVARIANT HAMILTONIANS
title_short On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_full On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_fullStr On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_full_unstemmed On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
title_sort On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space
dc.creator.none.fl_str_mv Falomir, Horacio Alberto
González Pisani, Pablo Andrés
Vega, Federico Gaspar
Cárcamo, D.
Méndez, F.
Loewe, M.
author Falomir, Horacio Alberto
author_facet Falomir, Horacio Alberto
González Pisani, Pablo Andrés
Vega, Federico Gaspar
Cárcamo, D.
Méndez, F.
Loewe, M.
author_role author
author2 González Pisani, Pablo Andrés
Vega, Federico Gaspar
Cárcamo, D.
Méndez, F.
Loewe, M.
author2_role author
author
author
author
author
dc.subject.none.fl_str_mv NONCOMMUTATIVE PHASE SPACE
QUANTUM MECHANICS
SPECTRUM OF ROTATIONALLY INVARIANT HAMILTONIANS
topic NONCOMMUTATIVE PHASE SPACE
QUANTUM MECHANICS
SPECTRUM OF ROTATIONALLY INVARIANT HAMILTONIANS
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras sl (2, ?) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
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: González Pisani, Pablo Andrés. 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: Cárcamo, D.. Universidad de Santiago de Chile; Chile
Fil: Méndez, F.. Universidad de Santiago de Chile; Chile
Fil: Loewe, M.. Pontificia Universidad Católica de Chile; Chile
description We study two-dimensional Hamiltonians in phase space with noncommutativity both in coordinates and momenta. We consider the generator of rotations on the noncommutative plane and the Lie algebra generated by Hermitian rotationally invariant quadratic forms of noncommutative dynamical variables. We show that two quantum phases are possible, characterized by the Lie algebras sl (2, ?) or su(2) according to the relation between the noncommutativity parameters, with the rotation generator related with the Casimir operator. From this algebraic perspective, we analyze the spectrum of some simple models with nonrelativistic rotationally invariant Hamiltonians in this noncommutative phase space, such as the isotropic harmonic oscillator, the Landau problem and the cylindrical well potential.
publishDate 2016
dc.date.none.fl_str_mv 2016-01
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/11336/54415
Falomir, Horacio Alberto; González Pisani, Pablo Andrés; Vega, Federico Gaspar; Cárcamo, D.; Méndez, F.; et al.; On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 49; 1; 1-2016; 55202-55248
1751-8113
CONICET Digital
CONICET
url http://hdl.handle.net/11336/54415
identifier_str_mv Falomir, Horacio Alberto; González Pisani, Pablo Andrés; Vega, Federico Gaspar; Cárcamo, D.; Méndez, F.; et al.; On the algebraic structure of rotationally invariant two-dimensional Hamiltonians on the noncommutative phase space; IOP Publishing; Journal of Physics A: Mathematical and Theoretical; 49; 1; 1-2016; 55202-55248
1751-8113
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/5/055202
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
application/pdf
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
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 13.22299

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