Path Integral Quantization of Doubly Supersymmetric Model

Hanaa Abdulkareem Elegla,Nasser Ismail Farahat

doi:10.4236/jamp.2022.102018

Abstract

The Hamilton-Jacobi formalism is used to discuss the path integral quantization of the double supersymmetric models with the spinning superparticle in the component and superfield form. The equations of motion are obtained as total differential equations in many variables. The equations of motion are integrable, and the path integral is obtained as an integration over the canonical phase space coordinates.

Highlights

Supersymmetric particles “superparticles” were stimulated by dynamical developing research in the supersymmetry in the present decade with such new models presented by: Brink-Schwarz [1] and Siegel [2]
The advantage of the Hamilton-Jacobi formalism is that we have no difference between first and second class constraints and we do not need gauge-fixing term to reduce or enlarge the physical phase-space
We have addressed the path integral quantization for constrained systems, to the derivation of quantum physics from classical physics

Summary

Introduction

Supersymmetric particles “superparticles” were stimulated by dynamical developing research in the supersymmetry in the present decade with such new models presented by: Brink-Schwarz [1] and Siegel [2]. When the constrained dynamical system possesses some second-class constraints there exists another method given by Batalain and Fradkin the BFV-BRST operator quantization method, which implies extending the initial phase space by auxiliary variables to convert the original second-class constraints into effective first-class ones in the extended manifold. The advantage of the Hamilton-Jacobi formalism is that we have no difference between first and second class constraints and we do not need gauge-fixing term to reduce or enlarge the physical phase-space.

Hamilton-Jacobi Formalism of Constrained Systems

Hamilton-Jacobi Formulation of Doubly Supersymmetric Models

Conclusion