On the k-symplectic, k-cosymplectic and multisymplectic formalisms of classical field theories
The objective of this work is twofold: First, we analyze the relation between the kcosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplec...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2007 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/1054 |
| Acceso en línea: | https://hdl.handle.net/2117/1054 |
| Access Level: | acceso abierto |
| Palabra clave: | Differential geometry Field theory (Physics) k-cosymplectic manifolds k-symplectic manifolds multisymplectic manifolds Lagrangian and Hamiltonian field theories Varietats simplèctiques Camps, Teoria dels (Física) Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories |
| Sumario: | The objective of this work is twofold: First, we analyze the relation between the kcosymplectic and the k-symplectic Hamiltonian and Lagrangian formalisms in classical field theories. In particular, we prove the equivalence between k-symplectic field theories and the so-called autonomous k-cosymplectic field theories, extending in this way the description of the symplectic formalism of autonomous systems as a articular case of the cosymplectic formalism in non-autonomous mechanics. Furthermore, we clarify some aspects of the geometric character of the solutions to the Hamilton-de Donder-Weyl and the Euler-Lagrange equations in these formalisms. Second, we study the equivalence between k-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangian field theories (those where the configuration bundle of the theory is trivial). |
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