Unified Lorentz-covariant Poisson Bracket for the Electrodynamics of a Point Particle
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914354871402496 |
|---|---|
| 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 |