Hamilton-Jacobi Approach for First Order Actions and Theories with Higher Derivatives

TL;DR

This paper explores Hamilton-Jacobi formalism adaptations for systems with higher derivative Lagrangians, comparing two approaches and analyzing examples to understand their differences and applications.

Contribution

It introduces and compares two Hamilton-Jacobi approaches for higher derivative theories, including degenerate cases, with detailed example analysis.

Findings

Both approaches are applicable to higher derivative systems.

Degenerate coordinate cases require special treatment.

Comparison clarifies the strengths and limitations of each method.

Abstract

In this work we analyze systems described by Lagrangians with higher order derivatives in the context of the Hamilton-Jacobi formalism for first order actions. Two different approaches are studied here: the first one is analogous to the description of theories with higher derivatives in the hamiltonian formalism according to [Sov. Phys. Journ. 26 (1983) 730; the second treats the case where degenerate coordinate are present, in an analogy to reference [Nucl. Phys. B 630 (2002) 509]. Several examples are analyzed where a comparison between both approaches is made.