Faddeev-Senjanovic Quantization of Supersymmetrical Electrodynamical System

TL;DR

This paper applies Faddeev-Senjanovic path integral quantization to a supersymmetrical electrodynamical system, simplifying the process by deriving gauge conditions and constraints directly from the system’s equations.

Contribution

It introduces a streamlined method for quantizing supersymmetrical electrodynamics using the Faddeev-Senjanovic scheme, avoiding step-by-step secondary constraint calculations.

Findings

Derived the generating functional of Green functions.

Constructed the gauge transformation generator.

Identified the secondary constraint as the electro-charge conservation law.

Abstract

According to the method of path integral quantization for the canonical constrained system in Faddeev-Senjanovic scheme, we quantize the supersymmetrical electrodynamic system in general situation, and obtain the generating functional of Green function. Another first class constraint is obtained by making the linear combination of several primary constraints, the generator of gauge transformation is constructed, gauge transformations of the all different fields are deduced. Utilizing the consistency equation of gauge fixing condition we deduce another gauge fixing condition, and we find that the secondary constraint of the system is an Euler-Lagrange equation that is just electro-charge conversation law. Thus, we do not need to calculate the other secondary constraints step by step, and get no new constraints naturally. So, the Faddeev-Senjanovic path integral quantization of the supersymmetrical electrodynamical system is simplified.