Lagrangian and Hamiltonian formalism in Field Theory: a simple model (1005.2753v1)

Abstract: The static of smooth maps from the two-dimensional disc to a smooth manifold can be regarded as a simplified version of the Classical Field Theory. In this paper we construct the Tulczyjew triple for the problem and describe the Lagrangian and Hamiltonian formalism. We outline also natural generalizations of this approach to arbitrary dimensions.