Brackets in multicontact geometry and multisymplectization
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914380349702144 |
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| author | de León, Manuel Izquierdo-López, Rubén Rivas, Xavier |
| author_facet | de León, Manuel Izquierdo-López, Rubén Rivas, Xavier |
| contents | In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2505_13224 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Brackets in multicontact geometry and multisymplectization de León, Manuel Izquierdo-López, Rubén Rivas, Xavier Differential Geometry Mathematical Physics 53D42, 70S20, 35B06, 53D10, 53Z05, 70S10 In this paper we introduce a graded bracket of forms on multicontact manifolds. This bracket satisfies a graded Jacobi identity as well as two different versions of the Leibniz rule, one of them being a weak Leibniz rule, extending the well-known notions in contact geometry. In addition, we develop the multisymplectization of multicontact structures to relate these brackets to the ones present in multisymplectic geometry and obtain the field equations in an abstract context. The Jacobi bracket also permits to study the evolution of observables and study the dissipation phenomena, which we also address. Finally, we apply the results to classical dissipative field theories. |
| title | Brackets in multicontact geometry and multisymplectization |
| topic | Differential Geometry Mathematical Physics 53D42, 70S20, 35B06, 53D10, 53Z05, 70S10 |
| url | https://arxiv.org/abs/2505.13224 |