Modified Hamiltonian formalism for higher-derivative theories

TL;DR

This paper introduces a modified Hamiltonian formalism for higher-derivative theories that simplifies the Legendre transformation and yields correct equations of motion without extra multipliers, applicable to both regular and singular Lagrangians.

Contribution

It proposes a new Hamiltonian approach for higher-derivative theories that improves upon Ostrogradski's method by simplifying transformations and ensuring proper equations of motion.

Findings

The formalism yields proper equations of motion without extra Lagrange multipliers.

The Legendre transformation is straightforward for nonsingular Lagrangians.

The approach extends to singular Lagrangians and field theories.

Abstract

The alternative version of Hamiltonian formalism for higher-derivative theories is proposed. As compared with the standard Ostrogradski approach it has the following advantages: (i) the Lagrangian, when expressed in terms of new variables yields proper equations of motion; no additional Lagrange multipliers are necessary (ii) the Legendre transformation can be performed in a straightforward way provided the Lagrangian is nonsingular in Ostrogradski sense. The generalization to singular Lagrangians as well as field theory are presented.