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arXiv · 2509.07358

Unified Lorentz-covariant Poisson Bracket for the Electrodynamics of a Point Particle

José Francisco Pérez-Barragán
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Abstract

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.

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José Francisco Pérez-Barragán. 2025-09-09. Unified Lorentz-covariant Poisson Bracket for the Electrodynamics of a Point Particle. https://doi.org/10.1007/s10773-025-06230-z

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