Augmented Superfield Approach To Unique Nilpotent Symmetries For Complex Scalar Fields In QED

TL;DR

This paper develops an augmented superfield approach to derive and interpret the unique nilpotent BRST and anti-BRST symmetries for complex scalar matter fields in 4D QED, addressing a longstanding problem.

Contribution

It introduces a new restriction on the supermanifold within the superfield formalism to derive exact nilpotent symmetries for matter fields in gauge theories.

Findings

Derived exact nilpotent symmetries for complex scalar fields in QED.

Provided geometric interpretations of the BRST symmetries.

Extended superfield formalism with a new supermanifold restriction.

Abstract

The derivation of the exact and unique nilpotent Becchi-Rouet-Stora-Tyutin (BRST)- and anti-BRST symmetries for the matter fields, present in any arbitrary interacting gauge theory, has been a long-standing problem in the framework of superfield approach to BRST formalism. These nilpotent symmetry transformations are deduced for the four (3 + 1)-dimensional (4D) complex scalar fields, coupled to the U(1) gauge field, in the framework of augmented superfield formalism. This interacting gauge theory (i.e. QED) is considered on a six (4, 2)-dimensional supermanifold parametrized by four even spacetime coordinates and a couple of odd elements of the Grassmann algebra. In addition to the horizontality condition (that is responsible for the derivation of the exact nilpotent symmetries for the gauge field and the (anti-)ghost fields), a new restriction on the supermanifold, owing its origin to the (super) covariant derivatives, has been invoked for the derivation of the exact nilpotent symmetry transformations for the matter fields. The geometrical interpretations for all the above nilpotent symmetries are discussed, too.