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

Cecile Barbachoux, Monika E. Pietrzyk, Igor V. Kanatchikov, Valery A. Kholodnyi and Joseph Kouneiher ()
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Cecile Barbachoux: Sciences and Technologies Department, INSPE, Cote d’Azur University, 06000 Nice, France
Monika E. Pietrzyk: Mathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UK
Igor V. Kanatchikov: National Quantum Information Centre KCIK, 80-309 Gdansk, Poland
Valery A. Kholodnyi: Wolfgang Pauli Institute, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria
Joseph Kouneiher: Sciences and Technologies Department, INSPE, Cote d’Azur University, 06000 Nice, France

Mathematics, 2025, vol. 13, issue 2, 1-14

Abstract: 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.

Keywords: covariant Hamilton–Jacobi; Maxwell equations; De Donder–Weyl Hamiltonian formalism; Dirac brackets; polysymplectic structure; canonical Hamilton–Jacobi (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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