Unique Nilpotent Symmetry Transformations For Matter Fields In QED: Augmented Superfield Formalism

TL;DR

This paper develops a superfield formalism to derive unique, off-shell nilpotent (anti-)BRST symmetry transformations for matter fields in QED, providing a geometric understanding within an extended supermanifold framework.

Contribution

It introduces a new gauge invariant condition on a supermanifold to obtain unique nilpotent symmetry transformations for all fields in QED, including matter fields, within the augmented superfield approach.

Findings

Derived exact (anti-)BRST transformations for QED matter fields.

Provided geometric interpretation of the symmetry transformations.

Established a new gauge invariant condition on the supermanifold.

Abstract

We derive the local, covariant, continuous, anticommuting and off-shell nilpotent (anti-)BRST symmetry transformations for the interacting U(1) gauge theory of quantum electrodynamics (QED) in the framework of augmented superfield approach to BRST formalism. In addition to the horizontality condition, we invoke another gauge invariant condition on the six (4, 2)-dimensional supermanifold to obtain the exact and unique nilpotent symmetry transformations for all the basic fields, present in the (anti-)BRST invariant Lagrangian density of the physical four (3 + 1)-dimensional QED. The above supermanifold is parametrized by four even spacetime variables x^\mu (with \mu = 0, 1, 2, 3) and a couple of odd variables (\theta and \bar\theta) of the Grassmann algebra. The new gauge invariant condition on the supermanifold owes its origin to the (super) covariant derivatives and leads to the derivation of unique nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above off-shell nilpotent transformations are discussed, too.