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We exploit the strength of the superspace (SUSP) unitary operator to obtainthe results of the application of the horizontality condition (HC) within theframework of augmented version of superfield formalism that is applied to theinteracting systems of Abelian 1-form gauge theories where the U(1) Abelian1-form gauge field couples to the Dirac and complex scalar fields in thephysical four (3 + 1)-dimensions of spacetime. These interacting theories aregeneralized onto a (4, 2)-dimensional supermanifold that is parametrized by thefour (3 + 1)-dimensional (4D) spacetime variables and a pair of Grassmannianvariables. To derive the (anti-)BRST symmetries for the matter fields, weimpose the gauge invariant restrictions (GIRs) on the superfields defined onthe (4, 2)-dimensional supermanifold. We discuss various outcomes that emergeout from our knowledge of the SUSP unitary operator and its hermitianconjugate. The latter operator is derived without imposing any operation ofhermitian conjugation on the parameters and fields of our theory from outside.This is an interesting observation in our present investigation.

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