Superspace Unitary Operator in QED with Dirac and Complex Scalar Fields: Superfield Approach

TL;DR

This paper employs the superspace unitary operator within an augmented superfield formalism to derive (anti-)BRST symmetries for matter fields in Abelian gauge theories coupled to Dirac and scalar fields, revealing novel hermitian properties.

Contribution

It introduces a new approach using the superspace unitary operator to obtain BRST symmetries without external hermitian conjugation, enhancing understanding of gauge-matter interactions.

Findings

Derived (anti-)BRST symmetries for matter fields.

Showed hermitian conjugate of the SUSP operator can be obtained intrinsically.

Extended the superfield formalism to include matter-gauge interactions.

Abstract

We exploit the strength of the superspace (SUSP) unitary operator to obtain the results of the application of the horizontality condition (HC) within the framework of augmented version of superfield formalism that is applied to the interacting systems of Abelian 1-form gauge theories where the U(1) Abelian 1-form gauge field couples to the Dirac and complex scalar fields in the physical four (3 + 1)-dimensions of spacetime. These interacting theories are generalized onto a (4, 2)-dimensional supermanifold that is parametrized by the four (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannian variables. To derive the (anti-)BRST symmetries for the matter fields, we impose the gauge invariant restrictions (GIRs) on the superfields defined on the (4, 2)-dimensional supermanifold. We discuss various outcomes that emerge out from our knowledge of the SUSP unitary operator and its hermitian conjugate. The latter operator is derived without imposing any operation of hermitian conjugation on the parameters and fields of our theory from outside. This is an interesting observation in our present investigation.