Tulczyjew's triples and lagrangian submanifolds in classical field theories

TL;DR

This paper extends Tulczyjew's triples from classical mechanics to classical field theories using multisymplectic formalism, providing a geometric framework where dynamical equations are represented as lagrangian submanifolds.

Contribution

It introduces a multisymplectic geometric approach to classical field theories, generalizing Tulczyjew's triples and defining lagrangian submanifolds in this context.

Findings

Dynamical equations are characterized as lagrangian submanifolds.

Extension of Tulczyjew's triples to multisymplectic formalism.

Provides a geometric interpretation of field equations.

Abstract

In this paper the notion of Tulczyjew's triples in classical mechanics is extended to classical field theories, using the so-called multisymplectic formalism, and a convenient notion of lagrangian submanifold in multisymplectic geometry. Accordingly, the dynamical equations are interpreted as the local equations defining these lagrangian submanifolds.