Gauge reduction in covariant field theory
In this work we develop a Lagrangian reduction theory for covariant field theories with local symmetries and, more specifically, with gauge symmetries. We model these symmetries by using a Lie group fiber bundle acting fiberwisely on the corresponding configuration bundle. In order to reduce the var...
| Autores: | , |
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| Formato: | artículo |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad Complutense de Madrid (UCM) |
| Repositorio: | Docta Complutense |
| Idioma: | inglés |
| OAI Identifier: | oai:docta.ucm.es:20.500.14352/71670 |
| Acesso em linha: | https://hdl.handle.net/20.500.14352/71670 |
| Access Level: | acceso abierto |
| Palavra-chave: | 530.1 Covariant reduction: Euler-Lagrange equations Gauge symmetry Generalized principal bundle Lagrangian field theory Noether theorem Física matemática |
| Resumo: | In this work we develop a Lagrangian reduction theory for covariant field theories with local symmetries and, more specifically, with gauge symmetries. We model these symmetries by using a Lie group fiber bundle acting fiberwisely on the corresponding configuration bundle. In order to reduce the variational principle, we utilize generalized principal connections, a type of Ehresmann connections that are equivariant by the fiberwise action. After obtaining the reduced equations, we give the reconstruction condition and we relate the vertical reduced equation with the Noether theorem. Lastly, we illustrate the theory by applying it to several examples, including the classical case (Lagrange-Poincaré reduction) and electromagnetism. |
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