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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Accesso online: | https://arxiv.org/abs/2509.07358 |
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| _version_ | 1866914354871402496 |
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| author | Pérez-Barragán, José Francisco |
| author_facet | Pérez-Barragán, José Francisco |
| contents | Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard formulations of field theories. To this end, it is necessary to translate the multisymplectic description of the system to the field's momentum representation, where a bilinear and Lorentz-covariant form emerges in a straightforward manner. Consequently, we establish a description for a system consisting of an electromagnetic field and a point particle interacting with each other that is based on a single Lorentz-covariant Poisson bracket with respect to all the canonical variables of the system. The results obtained from this proposal offer a solid foundation for the development of a Lorentz-covariant quantization process. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_07358 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unified Lorentz-covariant Poisson Bracket for the Electrodynamics of a Point Particle Pérez-Barragán, José Francisco Mathematical Physics Using the multisymplectic Hamiltonian formalism, we propose a Poisson bracket for the electromagnetic field that, in addition to satisfying the restricted principle of relativity, reproduces well-established results from the standard formulations of field theories. To this end, it is necessary to translate the multisymplectic description of the system to the field's momentum representation, where a bilinear and Lorentz-covariant form emerges in a straightforward manner. Consequently, we establish a description for a system consisting of an electromagnetic field and a point particle interacting with each other that is based on a single Lorentz-covariant Poisson bracket with respect to all the canonical variables of the system. The results obtained from this proposal offer a solid foundation for the development of a Lorentz-covariant quantization process. |
| title | Unified Lorentz-covariant Poisson Bracket for the Electrodynamics of a Point Particle |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2509.07358 |