^{1}

^{1}

^{1,2}

^{1}

^{2}

^{3}.

We exploit the key concepts of the augmented version of superfield approach to Becchi-Rouet-Stora-Tyutin (BRST) formalism to derive the superspace (SUSP)

A

The USF [

The purpose of our present investigation is to exploit the theoretical strength of AVSF to derive the superspace

In our present investigation, we have derived the

Our present investigation is essential on the following key considerations. First and foremost, as we have shown the

The contents of our present investigation are organized as follows. In Section

To begin with, we discuss here the nilpotent

We now focus our attention on the (anti-)dual-BRST symmetry transformations for the modified version of 2D Proca theory (with mass parameter

Another modified version of the 2D Abelian 1-form model is the bosonized version of anomalous Abelian 1-form gauge theory which is described by the following (anti-)BRST invariant Lagrangian density (see, e.g., [

Finally, we concentrate on a theoretically interesting system of the Abelian 1-form model of the 2D self-dual bosonic field theory which is described by the following (anti-)BRST invariant Lagrangian density (see, e.g., [

The decisive features of the (anti-)dual-BRST [i.e., (anti-)co-BRST] symmetry transformations are the observations that (i) they are nilpotent of order two (i.e.,

We briefly discuss here the derivation of the (anti-)co-BRST symmetries of our 1-form gauge theories by exploiting the geometrical superfield approach to BRST formalism [

We resort to the additional restrictions on the supervariables that are motivated by the basic requirements of AVSF which state that the (anti-)co-BRST invariant quantities should be independent of the “soul” coordinates. In this connection, we observe the following:

We now focus on the derivation of the (anti-)co-BRST symmetry transformations (

At this stage, we would like to clarify some of the

The above relations do

To determine the (anti-)dual-BRST symmetry transformations for the

We are now in the position to discuss the superfield approach to the derivation of the (anti-)co-BRST symmetries for the 2D self-dual chiral bosonic field theory. First of all, we generalize the relevant fields of the 2D theory onto the

Ultimately, we concentrate on the following (anti-)co-BRST invariance:

The precise expressions for the SUSP

We focus, first of all, on the derivation of the (anti-)co-BRST symmetry transformations for the 1D rigid rotor where the form of the unitary operator and its Hermitian conjugate is the same as given in (

In the above, we have constructed a 1-form

We have to express the superexpansion of

We concentrate now on the modified version of 2D Proca theory as well as the anomalous gauge theory and express the DHC and DGIRs in terms of the SUSP

Let us express the superfield

A close look and careful observations of (

Finally, we focus on the alternative to the DHC and DGIRs in the context of 2D self-dual bosonic field theory. Here the SUSP

We observe that

For the Abelian 1-form

We would like to dwell a bit on the

In our present endeavor, we have applied the AVSF to derive the (anti-)co-BRST symmetry transformations for a

We would like to lay emphasis on the fact that the models of the Abelian 1-form gauge theories in 1D and 2D (which have been considered in our present endeavor) are

We have succeeded in obtaining

The authors declare that they have no competing interests.

One of the authors (T. Bhanja) would like to gratefully acknowledge the financial support from CSIR, Govt. of India, New Delhi, under its SRF-scheme. Another author (N. Srinivas) is grateful to the BHU-fellowship for financial support. The present investigation has been carried out under the above financial support.