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...

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Detalles Bibliográficos
Autores: Román Roy, Narciso|||0000-0003-3663-9861, Rey, Angel M., Salgado, Modesto, Vilariño, Silvia
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
Descripción
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).