Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory

Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory

The covariant Hamilton–Jacobi formulation of electrodynamics is systematically derived from the first-order (Palatini-like) Lagrangian. This derivation utilizes the De Donder–Weyl covariant Hamiltonian formalism with constraints incroporating generalized Dirac brackets of forms and the associated po...

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Bibliographic Details
Main Authors: Cecile Barbachoux, Monika E. Pietrzyk, Igor V. Kanatchikov, Valery A. Kholodnyi, Joseph Kouneiher
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Mathematics
Subjects:
covariant Hamilton–Jacobi
Maxwell equations
De Donder–Weyl Hamiltonian formalism
Dirac brackets
polysymplectic structure
canonical Hamilton–Jacobi
Online Access:https://www.mdpi.com/2227-7390/13/2/283
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Summary:The covariant Hamilton–Jacobi formulation of electrodynamics is systematically derived from the first-order (Palatini-like) Lagrangian. This derivation utilizes the De Donder–Weyl covariant Hamiltonian formalism with constraints incroporating generalized Dirac brackets of forms and the associated polysymplectic reduction, which ensure manifest covariance and consistency with the field dynamics. It is also demonstrated that the canonical Hamilton–Jacobi equation in variational derivatives and the Gauss law constraint are derived from the covariant De Donder–Weyl Hamilton–Jacobi formulation after space + time decomposition.
ISSN:2227-7390

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