A description of classical field equations using extensions of graded Poisson brackets
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866915373564035072 |
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| author | de León, Manuel Izquierdo-López, Rubén |
| author_facet | de León, Manuel Izquierdo-López, Rubén |
| contents | As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these extensions can be used to obtain the field equations of a particular theory as well as the evolution of forms of arbitrary order, in a similar way that ordinary Poisson brackets provide in mechanics. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_04743 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A description of classical field equations using extensions of graded Poisson brackets de León, Manuel Izquierdo-López, Rubén Mathematical Physics 53D42, 53Z05, 35B06, 70S20 As it is well-known, Poisson brackets play a fundamental role both in mechanics and in classical field theories. In this paper we develop a theory of extensions of graded Poisson brackets in graded Dirac manifolds. We then show how these extensions can be used to obtain the field equations of a particular theory as well as the evolution of forms of arbitrary order, in a similar way that ordinary Poisson brackets provide in mechanics. |
| title | A description of classical field equations using extensions of graded Poisson brackets |
| topic | Mathematical Physics 53D42, 53Z05, 35B06, 70S20 |
| url | https://arxiv.org/abs/2507.04743 |