Hamilton Lie algebroids over Dirac structures and sigma models
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arXiv
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866908991843467264 |
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| author | Ikeda, Noriaki |
| author_facet | Ikeda, Noriaki |
| contents | We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section are generalizations of a Hamiltonian G-space and a momentum map over a symplectic manifold. We show some properties of a new Hamiltonian Lie algebroid, and construct the mechanics with this structure as an application, which are sigma models called the gauged Poisson sigma model and the gauged Dirac sigma model. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2309_10996 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hamilton Lie algebroids over Dirac structures and sigma models Ikeda, Noriaki Differential Geometry High Energy Physics - Theory Mathematical Physics Symplectic Geometry We propose a Hamiltonian Lie algebroid and a momentum section over a Dirac structure as a generalization of a Hamiltonian Lie algebroid over a pre-symplectic manifold and one over a Poisson manifold. A Hamiltonian Lie algebroid and a momentum section are generalizations of a Hamiltonian G-space and a momentum map over a symplectic manifold. We show some properties of a new Hamiltonian Lie algebroid, and construct the mechanics with this structure as an application, which are sigma models called the gauged Poisson sigma model and the gauged Dirac sigma model. |
| title | Hamilton Lie algebroids over Dirac structures and sigma models |
| topic | Differential Geometry High Energy Physics - Theory Mathematical Physics Symplectic Geometry |
| url | https://arxiv.org/abs/2309.10996 |