Gauge reduction in covariant field theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917855905185792 |
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| author | López, Marco Castrillón Abella, Álvaro Rodríguez |
| author_facet | López, Marco Castrillón Abella, Álvaro Rodríguez |
| contents | In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a 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 with several examples, including the classical case (Lagrange-Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2202_04578 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Gauge reduction in covariant field theory López, Marco Castrillón Abella, Álvaro Rodríguez Differential Geometry Mathematical Physics Dynamical Systems 70S05, 70S10, 70S15 (Primary), 58E15, 53Z05 (Secondary) In this work, we develop a Lagrangian reduction theory for covariant field theories with gauge symmetries. These symmetries are modeled by a Lie group fiber bundle acting fiberwisely on a 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 with several examples, including the classical case (Lagrange-Poincaré reduction), Electromagnetism, symmetry-breaking and non-Abelian gauge theories. |
| title | Gauge reduction in covariant field theory |
| topic | Differential Geometry Mathematical Physics Dynamical Systems 70S05, 70S10, 70S15 (Primary), 58E15, 53Z05 (Secondary) |
| url | https://arxiv.org/abs/2202.04578 |