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
- Institución
- Universidad Nacional de La Plata
- OAI Identificador
- oai:sedici.unlp.edu.ar:10915/100984
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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 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/10915/100984 |
url |
http://sedici.unlp.edu.ar/handle/10915/100984 |
dc.language.none.fl_str_mv |
eng |
language |
eng |
dc.relation.none.fl_str_mv |
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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) |
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openAccess |
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http://creativecommons.org/licenses/by-nc-sa/4.0/ Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0) |
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application/pdf 1-20 |
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