Symplectic realizations and Lie groupoids in Poisson Electrodynamics
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866917576716582912 |
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| author | Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Vitale, Patrizia |
| author_facet | Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Vitale, Patrizia |
| contents | We define the gauge potentials of Poisson electrodynamics as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic realization. Finite gauge transformations are obtained by integrating the sections of the Lie algebroid to bisections of a symplectic groupoid, which form a one-parameter group of transformations, whose action on the fields of the theory is realized in terms of an action groupoid. A covariant electromagnetic two-form is obtained, together with a dual two-form, invariant under gauge transformations. The duality appearing in the picture originates from the existence of a pair of orthogonal foliations of the symplectic realization, which produce dual quotient manifolds, one related with space-time, the other with momenta. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2312_16308 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Symplectic realizations and Lie groupoids in Poisson Electrodynamics Di Cosmo, Fabio Ibort, Alberto Marmo, Giuseppe Vitale, Patrizia High Energy Physics - Theory Mathematical Physics We define the gauge potentials of Poisson electrodynamics as sections of a symplectic realization of the spacetime manifold and infinitesimal gauge transformations as a representation of the associated Lie algebroid acting on the symplectic realization. Finite gauge transformations are obtained by integrating the sections of the Lie algebroid to bisections of a symplectic groupoid, which form a one-parameter group of transformations, whose action on the fields of the theory is realized in terms of an action groupoid. A covariant electromagnetic two-form is obtained, together with a dual two-form, invariant under gauge transformations. The duality appearing in the picture originates from the existence of a pair of orthogonal foliations of the symplectic realization, which produce dual quotient manifolds, one related with space-time, the other with momenta. |
| title | Symplectic realizations and Lie groupoids in Poisson Electrodynamics |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2312.16308 |