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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2025-01-01
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| author | Cecile Barbachoux Monika E. Pietrzyk Igor V. Kanatchikov Valery A. Kholodnyi Joseph Kouneiher |
| author_facet | Cecile Barbachoux Monika E. Pietrzyk Igor V. Kanatchikov Valery A. Kholodnyi Joseph Kouneiher |
| author_sort | Cecile Barbachoux |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-88d316e922cc4c43bbc7da608dd416b1 |
| institution | Kabale University |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
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| series | Mathematics |
| spelling | doaj-art-88d316e922cc4c43bbc7da608dd416b12025-01-24T13:40:02ZengMDPI AGMathematics2227-73902025-01-0113228310.3390/math13020283Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi TheoryCecile Barbachoux0Monika E. Pietrzyk1Igor V. Kanatchikov2Valery A. Kholodnyi3Joseph Kouneiher4Sciences and Technologies Department, INSPE, Cote d’Azur University, 06000 Nice, FranceMathematics and Physical Sciences, University of Exeter, Exeter EX4 4QL, UKNational Quantum Information Centre KCIK, 80-309 Gdansk, PolandWolfgang Pauli Institute, Oskar-Morgenstern-Platz 1, 1090 Vienna, AustriaSciences and Technologies Department, INSPE, Cote d’Azur University, 06000 Nice, FranceThe 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.https://www.mdpi.com/2227-7390/13/2/283covariant Hamilton–JacobiMaxwell equationsDe Donder–Weyl Hamiltonian formalismDirac bracketspolysymplectic structurecanonical Hamilton–Jacobi |
| spellingShingle | Cecile Barbachoux Monika E. Pietrzyk Igor V. Kanatchikov Valery A. Kholodnyi Joseph Kouneiher Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory Mathematics covariant Hamilton–Jacobi Maxwell equations De Donder–Weyl Hamiltonian formalism Dirac brackets polysymplectic structure canonical Hamilton–Jacobi |
| title | Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory |
| title_full | Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory |
| title_fullStr | Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory |
| title_full_unstemmed | Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory |
| title_short | Covariant Hamilton–Jacobi Formulation of Electrodynamics via Polysymplectic Reduction and Its Relation to the Canonical Hamilton–Jacobi Theory |
| title_sort | covariant hamilton jacobi formulation of electrodynamics via polysymplectic reduction and its relation to the canonical hamilton jacobi theory |
| topic | covariant Hamilton–Jacobi Maxwell equations De Donder–Weyl Hamiltonian formalism Dirac brackets polysymplectic structure canonical Hamilton–Jacobi |
| url | https://www.mdpi.com/2227-7390/13/2/283 |
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