Lagrangian-Hamiltonian unified formalism for field theory

Details Lagrangian-Hamiltonian unified formalism for field theory Lagrangian-Hamiltonian unified formalism for field theory

2002-12-02

arxiv.org/abs/math-ph/0212002v2

J.Math.Phys. 45 (2004) 360-380

Physics

Mathematical Physics

LaTeX file, 23 pages. Minor changes have been made. References are updated

Scientific paper

10.1063/1.1628384

The Rusk-Skinner formalism was developed in order to give a geometrical unified formalism for describing mechanical systems. It incorporates all the characteristics of Lagrangian and Hamiltonian descriptions of these systems (including dynamical equations and solutions, constraints, Legendre map, evolution operators, equivalence, etc.). In this work we extend this unified framework to first-order classical field theories, and show how this description comprises the main features of the Lagrangian and Hamiltonian formalisms, both for the regular and singular cases. This formulation is a first step toward further applications in optimal control theory for PDE's.

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