2 research outputs found
Finite dimesional Hamiltonian formalism for gauge and field theories
We discuss in this paper the canonical structure of classical field theory in
finite dimensions within the {\it{pataplectic}} Hamiltonian formulation, where
we put forward the role of Legendre correspondance. We define the generalized
Poisson -brackets which are the analogues of the Poisson bracket
on forms. We formulate the equations of motion of forms in terms of
-brackets. As illustration of our formalism we present three
examples: the interacting scalar fields, conformal string theory and the
electromagnetic field.Comment: 52 pages. In this paper we give a more general hamiltonian
formulation for a gauge and field theories, it's an extension of our previous
paper math-ph/000402
Lagrangian-Hamiltonian unified formalism for field theory
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.Comment: LaTeX file, 23 pages. Minor changes have been made. References are
update