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

Author

Listed:
  • 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
    IAS Archimedes Project, 83700 Saint Raphael, France)

  • 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)

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.

Suggested Citation

  • Cecile Barbachoux & Monika E. Pietrzyk & Igor V. Kanatchikov & Valery A. Kholodnyi & Joseph Kouneiher, 2025. "Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory," Mathematics, MDPI, vol. 13(2), pages 1-14, January.
  • Handle: RePEc:gam:jmathe:v:13:y:2025:i:2:p:283-:d:1569019
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