Universal Superspace Unitary Operator for Some Interesting Abelian Models: Superfield Approach

TL;DR

This paper develops a universal superspace unitary operator within superfield formalism, enabling the derivation of BRST and anti-BRST symmetries for various Abelian gauge models, demonstrating its broad applicability and simplifying the symmetry derivation process.

Contribution

It introduces a universal superspace unitary operator applicable to multiple Abelian models, providing an alternative to traditional methods like horizontality condition and gauge invariant restrictions.

Findings

The superspace unitary operator is the same for all considered Abelian models.

The operator simplifies the derivation of BRST and anti-BRST symmetries.

Universality extends to 4D interacting Abelian gauge theories.

Abstract

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.