SU(2) particle sigma model: The role of contact symmetries in global quantization

In this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S , by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-in...

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Detalhes bibliográficos
Autores: Aldaya, Víctor, Guerrero, J., López-Ruiz, F. F., Cossío, F.
Tipo de documento: artigo
Estado:Versión aceptada para publicación
Data de publicação:2016
País:España
Recursos:Consejo Superior de Investigaciones Científicas (CSIC)
Repositório:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/384399
Acesso em linha:http://hdl.handle.net/10261/384399
Access Level:Acceso aberto
Palavra-chave:Nonlinear systems
Sigma model
Contact symmetries
Non-canonical quantization
Non trivial topology
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spelling SU(2) particle sigma model: The role of contact symmetries in global quantizationAldaya, VíctorGuerrero, J.López-Ruiz, F. F.Cossío, F.Nonlinear systemsSigma modelContact symmetriesNon-canonical quantizationNon trivial topologyIn this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S , by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-invariant at the classical level, although not necessarily the Lagrangian. Special attention is paid to the role played by the basic quantum commutators, which depart from the canonical, Heisenberg-Weyl ones, as well as the relationship between the integration measure in the Hilbert space of the system and the non-trivial topology of the configuration space. Also, the quantization on momentum space is briefly outlined. © 2016 IOP Publishing Ltd.Work partially supported by the Spanish MINECO and Junta de Andalucía, under projects FIS2014-57387-C3-1P and FIS2014-57387-C3-3P, and FQM219-FQM4496, respectively.IOP PublishingMinisterio de Economía y Competitividad (España)Junta de AndalucíaConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]2025202520162025info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Postprintinfo:eu-repo/semantics/acceptedVersionhttp://hdl.handle.net/10261/384399reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/MINECO//FIS2014-57387-C3-1-Pinfo:eu-repo/grantAgreement/MINECO//FIS2014-57387-C3-3-Phttp://dx.doi.org/10.1088/1751-8113/49/50/505201Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3843992026-05-22T06:33:51Z
dc.title.none.fl_str_mv SU(2) particle sigma model: The role of contact symmetries in global quantization
title SU(2) particle sigma model: The role of contact symmetries in global quantization
spellingShingle SU(2) particle sigma model: The role of contact symmetries in global quantization
Aldaya, Víctor
Nonlinear systems
Sigma model
Contact symmetries
Non-canonical quantization
Non trivial topology
title_short SU(2) particle sigma model: The role of contact symmetries in global quantization
title_full SU(2) particle sigma model: The role of contact symmetries in global quantization
title_fullStr SU(2) particle sigma model: The role of contact symmetries in global quantization
title_full_unstemmed SU(2) particle sigma model: The role of contact symmetries in global quantization
title_sort SU(2) particle sigma model: The role of contact symmetries in global quantization
dc.creator.none.fl_str_mv Aldaya, Víctor
Guerrero, J.
López-Ruiz, F. F.
Cossío, F.
author Aldaya, Víctor
author_facet Aldaya, Víctor
Guerrero, J.
López-Ruiz, F. F.
Cossío, F.
author_role author
author2 Guerrero, J.
López-Ruiz, F. F.
Cossío, F.
author2_role author
author
author
dc.contributor.none.fl_str_mv Ministerio de Economía y Competitividad (España)
Junta de Andalucía
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Nonlinear systems
Sigma model
Contact symmetries
Non-canonical quantization
Non trivial topology
topic Nonlinear systems
Sigma model
Contact symmetries
Non-canonical quantization
Non trivial topology
description In this paper we achieve the quantization of a particle moving on the SU(2) group manifold, that is, the three-dimensional sphere S , by using group-theoretical methods. For this purpose, a fundamental role is played by contact symmetries, i.e., symmetries that leave the Poincaré-Cartan form semi-invariant at the classical level, although not necessarily the Lagrangian. Special attention is paid to the role played by the basic quantum commutators, which depart from the canonical, Heisenberg-Weyl ones, as well as the relationship between the integration measure in the Hilbert space of the system and the non-trivial topology of the configuration space. Also, the quantization on momentum space is briefly outlined. © 2016 IOP Publishing Ltd.
publishDate 2016
dc.date.none.fl_str_mv 2016
2025
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Postprint
info:eu-repo/semantics/acceptedVersion
format article
status_str acceptedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/384399
url http://hdl.handle.net/10261/384399
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/MINECO//FIS2014-57387-C3-1-P
info:eu-repo/grantAgreement/MINECO//FIS2014-57387-C3-3-P
http://dx.doi.org/10.1088/1751-8113/49/50/505201
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.publisher.none.fl_str_mv IOP Publishing
publisher.none.fl_str_mv IOP Publishing
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
repository.name.fl_str_mv
repository.mail.fl_str_mv
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