Hamilton-Jacobi Quantization of Landau-Ginzburg Theory

TL;DR

This paper applies the Hamilton-Jacobi method to quantize the Landau-Ginzburg theory, providing a gauge-independent approach to constrained systems and deriving their path integrals.

Contribution

It introduces a Hamilton-Jacobi framework for quantizing constrained field theories without gauge fixing, specifically applied to Landau-Ginzburg models.

Findings

Derived the equations of motion as total differential equations in many variables.

Established integrability conditions without gauge fixing.

Obtained the path integral formulation for Landau-Ginzburg theory.

Abstract

We discuss the Hamilton-Jacobi approach for a constrained system. We obtain the equation of motion for a singular system as total differential equations in many variables. We investigate the integrability conditions without using any gauge fixing condition. The path integral quantization for systems with finite degrees of freedom is applied to the field theories with constraints. So, we apply the Hamilton-Jacobi quantization to obtain the path integral of the Landau-Ginzburg theory.