The Lagrangian-Hamiltonian Formalism for Higher Order Field Theories

TL;DR

This paper extends the Lagrangian-Hamiltonian formalism to higher order field theories on fiber bundles, providing a coordinate-free Hamiltonian framework that depends solely on the action functional, resolving longstanding ambiguities.

Contribution

It introduces a generalized, coordinate-free Hamiltonian formalism for higher order Lagrangian field theories, building on Skinner and Rusk's approach.

Findings

Provides a coordinate-free Hamiltonian formalism for higher order theories

Resolves ambiguity issues present in previous formalisms

Applicable to a broad class of higher order field theories

Abstract

We generalize the Lagrangian-Hamiltonian formalism of Skinner and Rusk to higher order field theories on fiber bundles. As a byproduct we solve the long standing problem of defining, in a coordinate free manner, a Hamiltonian formalism for higher order Lagrangian field theories. Namely, our formalism does only depend on the action functional and, therefore, unlike previously proposed ones, is free from any relevant ambiguity.