are completely [*novel*]{} results in our present investigation.

PACS numbers: 11.30.Pb; 03.65.-w; 11.30.-j\
[*[Keywords]{}*]{}: Superspace [*dual*]{} unitary operator; augmented version of superfield formalism; nilpotency and absolute anticommutativity properties; (anti-)dual BRST symmetry transformations; geometrical interpretations; 1D and 2D Abelian 1-form gauge theories

Introduction
============

A [*classical*]{} gauge theory is endowed with the local gauge symmetries which are generated by the [*first-class*]{} constraints in the terminology of Dirac’s prescription for the classification scheme \[1,2\]. Thus, one of the decisive features of a classical gauge theory is the existence of the first-class constraints on it. The above cited [*classical*]{} local gauge symmetries are traded with the [*quantum*]{} gauge \[i.e. (anti-)BRST\] symmetries within the framework of Becchi-Rouet-Stora-Tyutin (BRST) formalism. The existence of the Curci-Ferrari (CF) condition(s) \[3\] is one of the key signatures of a [*quantum*]{} gauge theory when it is BRST quantized. The geometrical superfield approach \[4-10\] to BRST formalism is one of the most elegant methods which leads to the derivation of the nilpotent and absolutely anticommuting (anti-)BRST transformations for a given $D$-dimensional gauge theory. In addition, this usual superfield formalism \[6-8\] also leads to the deduction of the (anti-)BRST invariant CF-conditions (which are the key signature of the [*quantum*]{} gauge theories). 