Artículo
Dirac approach to constrained submanifolds in a double loop group: From Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
Fecha de publicación:
09/2014
Editorial:
American Institute of Physics
Revista:
Journal of Mathematical Physics
ISSN:
0022-2488
Idioma:
Inglés
Tipo de recurso:
Artículo publicado
Clasificación temática:
Resumen
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.
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Citación
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; American Institute of Physics; Journal of Mathematical Physics; 55; 9; 9-2014; 1-20
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