k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations

Details k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations k-cosymplectic classical field theories: Tulczyjew, Skinner--Rusk and Lie-algebroid formulations

2006-02-14

arxiv.org/abs/math-ph/0602038v2

Physics

Mathematical Physics

This is a complete revised version of the former article: "k-cosymplectic formalism in classical field theory: the Skinner--Ru

Scientific paper

The k-cosymplectic Lagrangian and Hamiltonian formalisms of first-order field theories are reviewed and completed. In particular, they are stated for singular and almost-regular systems. Subsequently, several alternative formulations for k-cosymplectic first-order field theories are developed: First, generalizing the construction of Tulczyjew for mechanics, we give a new interpretation of the classical field equations in terms of certain submanifolds of the tangent bundle of the $k^1$-velocities of a manifold. Second, the Lagrangian and Hamiltonian formalisms are unified by giving an extension of the Skinner-Rusk formulation on classical mechanics. Finally, both formalisms are formulated in terms of Lie algebroids.

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