descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 01 Jan 2011Embargo end date: 01 Jan 2007 English Publisher:American Institute of Mathematical Sciences (AIMS)Journal:Journal of Geometric Mechanics, volume 3, pages 113-137 (issn: 1941-4897,

Authors: Román Roy, Narciso; Rey, Angel M.; Salgado, Modesto; Vilariño, Silvia;

doi: 10.3934/jgm.2011.3.113 , 10.3934/jgm.2011.3.112 , 10.48550/arxiv.0705.4364

arXiv: http://arxiv.org/abs/0705.4364

handle: 2117/13693 , 2117/1054

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

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Abstract

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).

25 pages

Related Organizations

Universitat Polite`cnica de Catalunya
Spain
University of Santiago de Compostela (USC)
Spain
University of A Coruña
Spain
University of Santiago de Compostela
Spain
Universitat Politècnica de Catalunya
Spain

Keywords

Field theory (Physics), Geometria diferencial, Camps, Classificació AMS::53 Differential geometry::53D Symplectic geometry, FOS: Physical sciences, Classificació AMS::53 Differential geometry::53D Symplectic geometry, contact geometry, contact geometry, k-cosymplectic manifolds, k-symplectic manifolds, :70 Mechanics of particles and systems::70S Classical field theories [Classificació AMS], Differential geometry, 70S05, 53D05, 53D10, Camps, Teoria dels (Física), Manifolds, Classificació AMS::70 Mechanics of particles and systems::70S Classical field theories, Mathematical Physics, Àrees temàtiques de la UPC::Matemàtiques i estadística, :Matemàtiques i estadística [Àrees temàtiques de la UPC], Mathematical Physics (math-ph), Lagrangian and Hamiltonian field theories, :53 Differential geometry::53D Symplectic geometry, contact geometry [Classificació AMS], multisymplectic manifolds, Teoria dels (Física), Varietats simplèctiques

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