A Geometric Hamilton-Jacobi Theory for Classical Field Theories

TL;DR

This paper extends the geometric Hamilton-Jacobi theory from classical mechanics to classical field theories using multisymplectic geometry and Ehresmann connections, providing a new formalism for analyzing field dynamics.

Contribution

It introduces a geometric Hamilton-Jacobi framework for classical field theories within multisymplectic geometry, advancing the theoretical understanding of field dynamics.

Findings

Develops a multisymplectic Hamilton-Jacobi formalism for field theories

Establishes a connection between Ehresmann connections and field dynamics

Provides a geometric approach to classical field equations

Abstract

In this paper we extend the geometric formalism of the Hamilton-Jacobi theory for hamiltonian mechanics to the case of classical field theories in the framework of multisymplectic geometry and Ehresmann connections.