The Hamilton-Jacobi Formalism for Higher Order Field Theories

TL;DR

This paper extends the geometric Hamilton-Jacobi formalism to higher order field theories with regular lagrangian density, providing a new framework for analyzing complex physical systems.

Contribution

It introduces a generalized Hamilton-Jacobi formalism for higher order field theories, exploring its dependence on lagrangian densities that produce identical Euler-Lagrange equations.

Findings

Formalism applicable to higher order field theories

Analysis of lagrangian density dependence

Extension of geometric Hamilton-Jacobi methods

Abstract

We extend the geometric Hamilton-Jacobi formalism for hamiltonian mechanics to higher order field theories with regular lagrangian density. We also investigate the dependence of the formalism on the lagrangian density in the class of those yelding the same Euler-Lagrange equations.