Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model

Autores
Montani, Hugo Santos; Zuccalli, Marcela
Año de publicación
2014
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
We study the restriction to a family of second class constrained submanifolds in the cotangent bundle of a double Lie group equipped with a 2-cocycle extended symplectic form to build the corresponding Dirac brackets. It is shown that, for 2-cocycle vanishing on each isotropic subspace of the associated Manin triple, the Dirac bracket contains no traces of the cocycle. We also investigate the restriction of the left translation action of the double Lie group on its cotangent bundle, where it fails to be a canonical transformation. However, the Hamiltonian symmetry is restored on some special submanifolds. The main application is to loop groups, showing that a WZNW-type model on the double Lie group with a quadratic Hamilton function in the momentum maps associated with the left translation action on the cotangent bundle with the canonical symplectic form, restricts to a collective system on some special submanifolds. There, the Lagrangian version coincides with the so-called Poisson-Lie σ-model.
Facultad de Ciencias Exactas
Materia
Matemática
Dirac method on double lie groups
Central extensions and loop groups
Wznw model
Poisson-lie sigma model
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:10915/100984

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spelling Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-modelMontani, Hugo SantosZuccalli, MarcelaMatemáticaDirac method on double lie groupsCentral extensions and loop groupsWznw modelPoisson-lie sigma modelWe study the restriction to a family of second class constrained submanifolds in the cotangent bundle of a double Lie group equipped with a 2-cocycle extended symplectic form to build the corresponding Dirac brackets. It is shown that, for 2-cocycle vanishing on each isotropic subspace of the associated Manin triple, the Dirac bracket contains no traces of the cocycle. We also investigate the restriction of the left translation action of the double Lie group on its cotangent bundle, where it fails to be a canonical transformation. However, the Hamiltonian symmetry is restored on some special submanifolds. The main application is to loop groups, showing that a WZNW-type model on the double Lie group with a quadratic Hamilton function in the momentum maps associated with the left translation action on the cotangent bundle with the canonical symplectic form, restricts to a collective system on some special submanifolds. There, the Lagrangian version coincides with the so-called Poisson-Lie σ-model.Facultad de Ciencias Exactas2014-09info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionArticulohttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdf1-20http://sedici.unlp.edu.ar/handle/10915/100984enginfo:eu-repo/semantics/altIdentifier/url/https://ri.conicet.gov.ar/11336/59289info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4895465info:eu-repo/semantics/altIdentifier/issn/0022-2488info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4895465info:eu-repo/semantics/altIdentifier/hdl/11336/59289info: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:UNLP2025-09-29T11:21:06Zoai:sedici.unlp.edu.ar:10915/100984Institucionalhttp://sedici.unlp.edu.ar/Universidad públicaNo correspondehttp://sedici.unlp.edu.ar/oai/snrdalira@sedici.unlp.edu.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:13292025-09-29 11:21:06.501SEDICI (UNLP) - Universidad Nacional de La Platafalse
dc.title.none.fl_str_mv Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
title Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
spellingShingle Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
Montani, Hugo Santos
Matemática
Dirac method on double lie groups
Central extensions and loop groups
Wznw model
Poisson-lie sigma model
title_short Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
title_full Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
title_fullStr Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
title_full_unstemmed Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
title_sort Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
dc.creator.none.fl_str_mv Montani, Hugo Santos
Zuccalli, Marcela
author Montani, Hugo Santos
author_facet Montani, Hugo Santos
Zuccalli, Marcela
author_role author
author2 Zuccalli, Marcela
author2_role author
dc.subject.none.fl_str_mv Matemática
Dirac method on double lie groups
Central extensions and loop groups
Wznw model
Poisson-lie sigma model
topic Matemática
Dirac method on double lie groups
Central extensions and loop groups
Wznw model
Poisson-lie sigma model
dc.description.none.fl_txt_mv We study the restriction to a family of second class constrained submanifolds in the cotangent bundle of a double Lie group equipped with a 2-cocycle extended symplectic form to build the corresponding Dirac brackets. It is shown that, for 2-cocycle vanishing on each isotropic subspace of the associated Manin triple, the Dirac bracket contains no traces of the cocycle. We also investigate the restriction of the left translation action of the double Lie group on its cotangent bundle, where it fails to be a canonical transformation. However, the Hamiltonian symmetry is restored on some special submanifolds. The main application is to loop groups, showing that a WZNW-type model on the double Lie group with a quadratic Hamilton function in the momentum maps associated with the left translation action on the cotangent bundle with the canonical symplectic form, restricts to a collective system on some special submanifolds. There, the Lagrangian version coincides with the so-called Poisson-Lie σ-model.
Facultad de Ciencias Exactas
description We study the restriction to a family of second class constrained submanifolds in the cotangent bundle of a double Lie group equipped with a 2-cocycle extended symplectic form to build the corresponding Dirac brackets. It is shown that, for 2-cocycle vanishing on each isotropic subspace of the associated Manin triple, the Dirac bracket contains no traces of the cocycle. We also investigate the restriction of the left translation action of the double Lie group on its cotangent bundle, where it fails to be a canonical transformation. However, the Hamiltonian symmetry is restored on some special submanifolds. The main application is to loop groups, showing that a WZNW-type model on the double Lie group with a quadratic Hamilton function in the momentum maps associated with the left translation action on the cotangent bundle with the canonical symplectic form, restricts to a collective system on some special submanifolds. There, the Lagrangian version coincides with the so-called Poisson-Lie σ-model.
publishDate 2014
dc.date.none.fl_str_mv 2014-09
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
Articulo
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info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://sedici.unlp.edu.ar/handle/10915/100984
url http://sedici.unlp.edu.ar/handle/10915/100984
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/11336/59289
info:eu-repo/semantics/altIdentifier/url/https://aip.scitation.org/doi/10.1063/1.4895465
info:eu-repo/semantics/altIdentifier/issn/0022-2488
info:eu-repo/semantics/altIdentifier/doi/10.1063/1.4895465
info:eu-repo/semantics/altIdentifier/hdl/11336/59289
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
1-20
dc.source.none.fl_str_mv reponame:SEDICI (UNLP)
instname:Universidad Nacional de La Plata
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instname_str Universidad Nacional de La Plata
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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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