Hamilton-Jacobi formulation for singular systems with second order Lagrangians

TL;DR

This paper extends the Hamilton-Jacobi formalism to singular systems with second order Lagrangians and demonstrates its application to Podolsky electrodynamics, comparing results with Dirac's method.

Contribution

It introduces a generalized Hamilton-Jacobi approach for second order singular systems and applies it to a specific physical theory, Podolsky electrodynamics.

Findings

Successful formulation of Hamilton-Jacobi for second order singular systems

Application to Podolsky electrodynamics with consistent results

Comparison with Dirac's method confirms validity

Abstract

Recently the Hamilton-Jacobi formulation for first order constrained systems has been developed. In such formalism the equations of motion are written as total differential equations in many variables. We generalize the Hamilton-Jacobi formulation for singular systems with second order Lagrangians and apply this new formulation to Podolsky electrodynamics, comparing with the results obtained through Dirac's method.