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, ℝ) 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.
Instituto de Física La Plata
Materia
Matemática
Física
Noncommutative phase space
Quantum mechanics
Spectrum of rotationally invariant hamiltonians
Nivel de accesibilidad
acceso abierto
Condiciones de uso
http://creativecommons.org/licenses/by-nc-sa/4.0/
Repositorio
SEDICI (UNLP)
Institución
Universidad Nacional de La Plata
OAI Identificador
oai:sedici.unlp.edu.ar:10915/99534
Acceder
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oai_identifier_str oai:sedici.unlp.edu.ar:10915/99534
network_acronym_str SEDICI
repository_id_str 1329
network_name_str SEDICI (UNLP)
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.MatemáticaFísicaNoncommutative phase spaceQuantum mechanicsSpectrum of rotationally invariant hamiltoniansWe 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, ℝ) 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.Instituto de Física La Plata2016-01info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf55202-55248http://sedici.unlp.edu.ar/handle/10915/99534enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/54415info:eu-repo/semantics/altIdentifier/issn/1751-8113info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/5/055202info:eu-repo/semantics/altIdentifier/hdl/11336/54415info:eu-repo/semantics/openAccesshttp://creativecommons.org/licenses/by-nc-sa/4.0/Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)reponame:SEDICI (UNLP)instname:Universidad Nacional de La Platainstacron:UNLP2025-10-15T11:12:05Zoai:sedici.unlp.edu.ar:10915/99534Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-10-15 11:12:05.558SEDICI (UNLP) - Universidad Nacional de La Platafalse
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
Matemática
Física
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 Matemática
Física
Noncommutative phase space
Quantum mechanics
Spectrum of rotationally invariant hamiltonians
topic Matemática
Física
Noncommutative phase space
Quantum mechanics
Spectrum of rotationally invariant hamiltonians
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, ℝ) 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.
Instituto de Física La Plata
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, ℝ) 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
Articulo
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://sedici.unlp.edu.ar/handle/10915/99534
url http://sedici.unlp.edu.ar/handle/10915/99534
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/54415
info:eu-repo/semantics/altIdentifier/issn/1751-8113
info:eu-repo/semantics/altIdentifier/doi/10.1088/1751-8113/49/5/055202
info:eu-repo/semantics/altIdentifier/hdl/11336/54415
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
eu_rights_str_mv openAccess
rights_invalid_str_mv http://creativecommons.org/licenses/by-nc-sa/4.0/
Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)
dc.format.none.fl_str_mv application/pdf
55202-55248
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
instacron:UNLP
reponame_str SEDICI (UNLP)
collection SEDICI (UNLP)
instname_str Universidad Nacional de La Plata
instacron_str UNLP
institution UNLP
repository.name.fl_str_mv SEDICI (UNLP) - Universidad Nacional de La Plata
repository.mail.fl_str_mv alira@sedici.unlp.edu.ar
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score 13.22299

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