Salvato in:
| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2312.17474 |
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Sommario:
- 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.