Hamilton-Jacobi quantization of singular Lagrangians with linear velocities

TL;DR

This paper explores the Hamilton-Jacobi method to quantize constrained Hamiltonian systems with linear velocities, focusing on integrability conditions to derive path integral quantization for singular Lagrangians.

Contribution

It introduces a Hamilton-Jacobi framework for quantizing singular Lagrangians with linear velocities, emphasizing integrability conditions for path integral formulation.

Findings

Derived conditions for integrability of equations of motion

Established path integral quantization method for singular Lagrangians

Extended Hamilton-Jacobi approach to constrained systems

Abstract

In this paper, constrained Hamiltonian systems with linear velocities are investigated by using the Hamilton-Jacobi method. We shall consider the integrablity conditions on the equations of motion and the action function as well in order to obtain the path integral quantization of singular Lagrangians with linear velocities.