Superfield Approach To Nilpotent Symmetries For QED From A Single Restriction: An Alternative To The Horizontality Condition

TL;DR

This paper introduces a novel superfield approach to derive BRST and anti-BRST symmetries in 4D QED using a single gauge-invariant restriction on a supermanifold, offering an alternative to the traditional horizontality condition.

Contribution

It presents a new single restriction method on a supermanifold to obtain nilpotent symmetries, generalizing the superfield formalism beyond the horizontality condition.

Findings

Derived BRST and anti-BRST transformations for QED fields.

Established a new gauge-invariant restriction on supermanifold.

Unified the derivation of symmetries under a single condition.

Abstract

We derive together the exact local, covariant, continuous and off-shell nilpotent Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for the U(1) gauge field (A_\mu), the (anti-)ghost fields ((\bar C)C) and the Dirac fields (\psi, \bar\psi) of the Lagrangian density of a four (3 + 1)-dimensional QED by exploiting a single restriction on the six (4, 2)-dimensional supermanifold. A set of four even spacetime coordinates x^\mu (\mu = 0, 1, 2, 3) and two odd Grassmannian variables \theta and \bar\theta parametrize this six dimensional supermanifold. The new gauge invariant restriction on the above supermanifold owes its origin to the (super) covariant derivatives and their intimate relations with the (super) 2-form curvatures (\tilde F^{(2)})F^{(2)} constructed with the help of (super) 1-form gauge connections (\tilde A^{(1)})A^{(1)} and (super) exterior derivatives (\tilde d)d. The results obtained separately by exploiting (i) the horizontality condition, and (ii) one of its consistent extensions, are shown to be a simple consequence of this new single restriction on the above supermanifold. Thus, our present endeavour provides an alternative to (and, in some sense, generalization of) the horizontality condition of the usual superfield formalism applied to the derivation of BRST symmetries.