On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

Details On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories On the k-Symplectic, k-Cosymplectic and Multisymplectic Formalisms of Classical Field Theories

2007-05-30

arxiv.org/abs/0705.4364v1

Physics

Mathematical Physics

25 pages

Scientific paper

The objective of this work is twofold: First, we analyze the relation between the k-cosymplectic 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 particular 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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