Hamilton-Jacobi treatment of fields with constraints

TL;DR

This paper applies Guler's Hamilton-Jacobi formalism to constrained field theories, explores integrability conditions, and performs path integral quantization, with detailed analysis of Proca's model.

Contribution

It extends Hamilton-Jacobi formalism to field theories with constraints and demonstrates its application through path integral quantization, including a detailed study of Proca's model.

Findings

Successful application of Hamilton-Jacobi formalism to constrained fields

Derivation of integrability conditions for the formalism

Quantization of Proca's model using the developed approach

Abstract

In this paper the $Guler's$ formalism for the systems with finite degrees of freedom is applied to the field theories with constraints. The integrability conditions are investigated and the path integral quantization is performed using the action given by Hamilton-Jacobi formulation. The Proca's model is investigated in details.