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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2312.17474 |
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| _version_ | 1866916076405653504 |
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| author | Pietrzyk, Monika E. Barbachoux, Cécile Kouneiher, Joseph |
| author_facet | Pietrzyk, Monika E. Barbachoux, Cécile Kouneiher, Joseph |
| contents | The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant (De Donder-Weyl) Hamilton-Jacobi equation, which is a partial derivative equation on a finite dimensional space of vector potentials and spacetime coordinates. We show that the procedure of spacetime splitting applied to the latter allows us to reproduce both the canonical Hamilton-Jacobi equation and the Gauss law constraint in the Hamilton-Jacobi form without a recourse to the canonical Hamiltonian analysis. Our consideration may help to analyze the quasi-classical limit of the connection between the standard quantization in field theory based on the canonical Hamiltonian formalism with a preferred time dimension and the precanonical quantization that uses the De Donder-Weyl Hamiltonian formulation where space and time dimensions treated equally. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_17474 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | The relation between the canonical Hamilton-Jacobi equation and the covariant Hamilton-Jacobi equation for Maxwell's electrodynamics Pietrzyk, Monika E. Barbachoux, Cécile Kouneiher, Joseph Mathematical Physics The aim of this paper is to understand the relation between the canonical Hamilton-Jacobi equation for Maxwell's electrodynamics, which is an equation with variational derivatives for a functional of field configurations, and the covariant (De Donder-Weyl) Hamilton-Jacobi equation, which is a partial derivative equation on a finite dimensional space of vector potentials and spacetime coordinates. We show that the procedure of spacetime splitting applied to the latter allows us to reproduce both the canonical Hamilton-Jacobi equation and the Gauss law constraint in the Hamilton-Jacobi form without a recourse to the canonical Hamiltonian analysis. Our consideration may help to analyze the quasi-classical limit of the connection between the standard quantization in field theory based on the canonical Hamiltonian formalism with a preferred time dimension and the precanonical quantization that uses the De Donder-Weyl Hamiltonian formulation where space and time dimensions treated equally. |
| title | The relation between the canonical Hamilton-Jacobi equation and the covariant Hamilton-Jacobi equation for Maxwell's electrodynamics |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2312.17474 |