Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
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 associ...
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| Autores principales: | , |
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| Formato: | Articulo |
| Lenguaje: | Inglés |
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2014
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| Acceso en línea: | http://sedici.unlp.edu.ar/handle/10915/100984 https://ri.conicet.gov.ar/11336/59289 https://aip.scitation.org/doi/10.1063/1.4895465 |
| Aporte de: |
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I19-R120-10915-100984 |
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| record_format |
dspace |
| institution |
Universidad Nacional de La Plata |
| institution_str |
I-19 |
| repository_str |
R-120 |
| collection |
SEDICI (UNLP) |
| language |
Inglés |
| topic |
Matemática Dirac method on double lie groups Central extensions and loop groups Wznw model Poisson-lie sigma model |
| spellingShingle |
Matemática Dirac method on double lie groups Central extensions and loop groups Wznw model Poisson-lie sigma model Montani, Hugo Santos Zuccalli, Marcela Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model |
| topic_facet |
Matemática Dirac method on double lie groups Central extensions and loop groups Wznw model Poisson-lie sigma model |
| 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. |
| format |
Articulo Articulo |
| author |
Montani, Hugo Santos Zuccalli, Marcela |
| author_facet |
Montani, Hugo Santos Zuccalli, Marcela |
| author_sort |
Montani, Hugo Santos |
| title |
Dirac approach to constrained submanifolds in a double loop group: from Wess-Zumino-Novikov-Witten to Poisson-Lie σ-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 |
| publishDate |
2014 |
| url |
http://sedici.unlp.edu.ar/handle/10915/100984 https://ri.conicet.gov.ar/11336/59289 https://aip.scitation.org/doi/10.1063/1.4895465 |
| work_keys_str_mv |
AT montanihugosantos diracapproachtoconstrainedsubmanifoldsinadoubleloopgroupfromwesszuminonovikovwittentopoissonliesmodel AT zuccallimarcela diracapproachtoconstrainedsubmanifoldsinadoubleloopgroupfromwesszuminonovikovwittentopoissonliesmodel |
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Repositorios |
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1764820440354652161 |