Lagrangian and Hamiltonian formalism in Field Theory:  A simple model

Katarzyna Grabowska

doi:10.3934/jgm.2010.2.375

Article Contents

2010, Volume 2, Issue 4: 375-395. Doi: 10.3934/jgm.2010.2.375

This issue Previous Article Variational integrators for discrete Lagrange problems Next Article Geometric Jacobian linearization and LQR theory

Lagrangian and Hamiltonian formalism in Field Theory: A simple model

Katarzyna Grabowska^1,

1.
Faculty of Physics, University of Warsaw, Hoza 69, 00-681 Warszawa

Received: June 30, 2010

Revised: October 31, 2010

Published: November 2010

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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.

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Mathematics Subject Classification: 70S05, 70H03, 70H05.

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