Hamilton-Jacobi Treatment of Constraint Field Systems

TL;DR

This paper applies the Hamilton-Jacobi approach to analyze the classical structure and quantization of three different constrained field systems, providing insights into their equations of motion and integrability conditions.

Contribution

It introduces a Hamilton-Jacobi framework for constrained fields and demonstrates its application to scalar-fermion, scalar-vector, and electromagnetic-spinor systems.

Findings

Derived equations of motion as total differential equations.

Investigated integrability conditions for the systems.

Quantized the second and third systems using path integral formulation.

Abstract

Motivated by the Hamilton$-$Jacobi approach of fields with constraints, we analyse the classical structure of three different constrained field systems: (i) the scalar field coupled to two flavors of fermions through Yukawa couplings (ii) the scalar field coupled minimally to the vector potential (iii) the electromagnetic field coupled to a spinor. The equations of motion are obtained as total differential equations in many variables. The integrability conditions are investigated. The second and third constrained systems are quantized using canonical path integral formulation based on the Hamilton$-$Jacobi treatment.