We discuss the BRST cohomology and exhibit a connection between the Hodge decomposition theorem and the topological properties of a two dimensional free non-Abelian gauge theory having no interaction with matter fields. The topological nature of this theory is encoded in the vanishing of the Laplacian operator when equations of motion are exploited. We obtain two sets of topological invariants ...

We discuss BRST and anti–BRST transformations for an Abelian antisymmetric gauge field in 4D and find that, in order for them to anticommute, we have to impose a condition on the auxiliary fields. This condition is similar to the Curci–Ferrari condition for the 4D non–Abelian 1-form gauge theories and represents a consistency requirement. We interpret it as a signal that our Abelian 2-form gaug...

A superspace formulation for the Batalin Vilkovisky formalism (also called fieldantifield quantization ) with extended BRST invariance (BRST and anti-BRST invariance ) for gauge theories with closed algebra is presented. In contrast to a recent formulation, where only BRST invariance holds off shell, two collective sets of fields are introduced and an off shell realization of the extended algeb...

Exploiting the theoretical potential of modified Bonora-Tonin superfield approach (MBTSA) as well (anti-)chiral (ACSA) to Becchi-Rouet-Stora-Tyutin (BRST) formalism, we derive complete set off-shell nilpotent (anti-)BRST symmetry transformations corresponding classical two- 1 + </mrow...

The quantum BRST anti BRST operators are explicitly derived and the consequences related to correlation functions are investigated. The connection with the standard formalism and the loopwise expansions for quantum operators and anomalies in Sp(2) approach are analyzed .

We demonstrate that the two (1 + 1)-dimensional (2D) free 1-form Abelian gauge theory provides an interesting field theoretical model for the Hodge theory. The physical symmetries of the theory correspond to all the basic mathematical ingredients that are required in the definition of the de Rham cohomological operators of the differential geometry. The conserved charges, corresponding to the a...

We show that any BRST invariant quantum action with open or closed gauge algebra has a corresponding local background gauge invariance. If the BRST symmetry is anomalous, but the anomaly can be removed in the antifield formalism, then the effective action possesses a local background gauge invariance. The presence of antifields (BRST sources) is necessary. As an example we analyze chiral W3 gra...

We discuss some aspects of the topological features of a non-interacting two (1 + 1)-dimensional Abelian gauge theory in the framework of superfield formalism. This theory is described by a BRST invariant Lagrangian density in the Feynman gauge. We express the local and continuous symmetries, Lagrangian density, topological invariants and symmetric energy momentum tensor of this theory in the l...