Lagrangian Reduction by Stages in Field Theory
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arXiv
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| Format: | Preprint |
| Published: |
2020
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| _version_ | 1866914408915009536 |
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| author | Berbel, Miguel Á. López, Marco Castrillón |
| author_facet | Berbel, Miguel Á. López, Marco Castrillón |
| contents | We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2007_14854 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Lagrangian Reduction by Stages in Field Theory Berbel, Miguel Á. López, Marco Castrillón Differential Geometry Mathematical Physics Primary 58E15, Secondary 37J37, 58D19, 70S05, 70S10 We propose a category of bundles in order to perform Lagrangian reduction by stages in covariant Field Theory. This category plays an analogous role to Lagrange-Poincaré bundles in Lagrangian reduction by stages in Mechanics and includes both jet bundles and reduced covariant configuration spaces. Furthermore, we analyze the resulting reconstruction condition and formulate the Noether theorem in this context. Finally, a model of a molecular strand with rotors is seen as an application of this theoretical frame. |
| title | Lagrangian Reduction by Stages in Field Theory |
| topic | Differential Geometry Mathematical Physics Primary 58E15, Secondary 37J37, 58D19, 70S05, 70S10 |
| url | https://arxiv.org/abs/2007.14854 |