Artigo Acesso aberto Revisado por pares

On the $k$-symplectic, $k$-cosymplectic and multisymplectic formalisms of classical field theories

2011; American Institute of Mathematical Sciences; Volume: 3; Issue: 1 Linguagem: Inglês

10.3934/jgm.2011.3.113

ISSN

1941-4897

Autores

Narciso Román‐Roy, A. Martı́n del Rey, Modesto Salgado, Silvia Vilariño,

Tópico(s)

Algebraic Geometry and Number Theory

Resumo

The objective of this work is twofold:First, we analyze the relation between the$k$-cosymplectic and the $k$-symplectic Hamiltonian and Lagrangianformalisms in classical field theories.In particular, we prove the equivalence between$k$-symplectic field theories andthe so-called autonomous $k$-cosymplectic field theories,extending in this way the description of the symplectic formalism of autonomous systems asa particular case of the cosymplectic formalism in non-autonomous mechanics.Furthermore, we clarify some aspects of thegeometric character of the solutions to theHamilton-de Donder-Weyl and the Euler-Lagrange equationsin these formalisms.Second, we study the equivalence between$k$-cosymplectic and a particular kind of multisymplectic Hamiltonian and Lagrangianfield theories (those where the configuration bundle of the theory is trivial).

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