On Higher Derivatives as Constraints in Field Theory: a Geometric Perspective

TL;DR

This paper provides a geometric formalization of how higher derivative field theories can be viewed as constrained first derivative theories within the Hamiltonian framework, offering new insights into their structure.

Contribution

It introduces a geometric approach to understanding higher derivative field theories as constrained first derivative systems in the Hamiltonian formalism.

Findings

Provides a geometric formalization of higher derivative theories.

Shows how these theories can be viewed as constrained first derivative systems.

Enhances understanding of the Hamiltonian formulation for complex field theories.

Abstract

We formalize geometrically the idea that the (de Donder) Hamiltonian formulation of a higher derivative Lagrangian field theory can be constructed understanding the latter as a first derivative theory subjected to constraints.