A Completely Invariant SUSY Transform of Supersymmetric QED

TL;DR

The paper develops a fully invariant supersymmetry transformation in SUSY QED that preserves gauge conditions and satisfies SUSY algebra, enabling derivation of Ward identities without ghost fields.

Contribution

It introduces a novel SUSY transformation that maintains gauge invariance and SUSY algebra in SUSY QED, avoiding ghost fields and ensuring consistency with gauge fixing.

Findings

Derived a SUSY transformation preserving Lorentz gauge.

Established Ward identities relating photon and photino propagators.

Ensured the transformation satisfies SUSY algebra modulo gauge terms.

Abstract

We study the SUSY breaking of the covariant gauge-fixing term in SUSY QED and observe that this corresponds to a breaking of the Lorentz gauge condition by SUSY. Reasoning by analogy with SUSY's violation of the Wess-Zumino gauge, we argue that the SUSY transformation, already modified to preserve Wess-Zumino gauge, should be further modified by another gauge transformation which restores the Lorentz gauge condition. We derive this modification and use the resulting transformation to derive a Ward identitiy relating the photon and photino propagators without using ghost fields. Our transformation also fulfills the SUSY algebra, modulo terms that vanish in Lorentz gauge.