Dirac approach to constrained submanifolds in a double loop group: From Wess-Zumino-Novikov-Witten to Poisson-Lie σ-model
| Autor: | Hugo Santos Montani, Marcela Zuccalli |
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| Rok vydání: | 2014 |
| Předmět: |
Matemáticas
DIRAC METHOD ON DOUBLE LIE GROUPS WZNW MODEL Canonical transformation Matemática Pura purl.org/becyt/ford/1 [https] symbols.namesake Quadratic equation Mathematics::Symplectic Geometry Mathematical Physics Mathematical physics Physics Matemática purl.org/becyt/ford/1.1 [https] POISSON-LIE SIGMA MODEL Lie group Statistical and Nonlinear Physics Central extensions and loop groups Poisson-lie sigma model CENTRAL EXTENSIONS AND LOOP GROUPS symbols Dirac method on double lie groups Cotangent bundle Hamiltonian (quantum mechanics) Wznw model CIENCIAS NATURALES Y EXACTAS Subspace topology Dirac bracket Symplectic geometry |
| Zdroj: | CONICET Digital (CONICET) Consejo Nacional de Investigaciones Científicas y Técnicas instacron:CONICET SEDICI (UNLP) Universidad Nacional de La Plata instacron:UNLP |
| ISSN: | 1089-7658 0022-2488 |
| DOI: | 10.1063/1.4895465 |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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