  Within the framework of augmented version of superfield formalism, we derive
the superspace unitary operator and show its usefulness in the derivation of
Becchi-Rouet-Stora-Tyutin (BRST) and anti-BRST symmetry transformations for a
set of interesting models for the Abelian 1-form gauge theories. These models
are (i) a one (0+1)-dimensional (1D) toy model of a rigid rotor, (ii) the two
(1+1)-dimensional (2D) modified versions of the Proca and anomalous Abelian
1-form gauge theories, and (iii) the 2D self-dual bosonic gauge field theory.
We provide, in some sense, the alternatives to the horizontality condition (HC)
and the gauge invariant restrictions (GIRs) in the language of the above
superspace (SUSP) unitary operator. One of the key observations of our present
endeavor is the result that the SUSP unitary operator and its hermitian
conjugate are found to be the same for all the Abelian models under
consideration (including the 4D interacting Abelian 1-form gauge theories with
Dirac and complex scalar fields which have been discussed earlier). Thus, we
establish the universality of the SUSP operator for the above Abelian theories.
