The Batalin–Vilkovisky formalism description of self-dual Chern–Simons gauge theory coupled to matter fields in superspace

We construct the extended BRST and anti-BRST transformation by considering a shift symmetry both in Abelian and non-Abelian Chern–Simons theories coupled to scalar fields using the approach of Batalin–Vilkovisky quantization. The extended BRST invariant Lagrangian density is able to be addressed in the framework of superfield formalism with one fermionic coordinate. In the case of extended BRST–anti-BRST symmetry, it is shown that the Batalin–Vilkovisky action of the theory can be expressed in a covariant form with two fermionic coordinates in the superspace.

Faddeev-Popov Ghost and BRST Symmetry in Yang-Mills Theory

Ghost fields arise from the quantization of the gauge field with constraints (gauge fixing) through the path integral method. By substituting a form of identity, an effective propagator will be obtained from the gauge field with constraints and this is called the Faddeev-Popov method. The Grassmann odd properties of the ghost field cause the gauge transformation parameter to be Grassmann odd, so a BRST transformation is defined. Ghost field emergence with Grassmann odd properties can also be obtained through the least action principle with gauge transformation, and thus the relations between the BRST transformation parameters and the ghost field is obtained.

Lorentz violating gaugeon formalism of Yang–Mills theory

VSR is a way of keeping the main relativistic effects intact using subgroups of the Lorentz group instead of the full Lorentz group itself. In this paper, we study the quantization of the Yang–Mills theory, gaugeon formalism within the VSR framework. The gauge freedom is restored once we develop the gaugeon formalism. Also, the mass of corresponding gauge boson is modified because of the VSR effect. We find that the gaugeon formalism for Yang–Mills theory in VSR is consistent with the Lorentz invariant case except the fact that each field gets mass. We also discuss the generalization of BRST transformation within VSR framework. It is found that the gaugeon modes appear in the configuration space through the Jacobian of functional measure.

Double Hodge Theory for a Particle on Torus

We investigate all possible nilpotent symmetries for a particle on torus. We explicitly construct four independent nilpotent BRST symmetries for such systems and derive the algebra between the generators of such symmetries. We show that such a system has rich mathematical properties and behaves as double Hodge theory. We further construct the finite field dependent BRST transformation for such systems by integrating the infinitesimal BRST transformation systematically. Such a finite transformation is useful in realizing the various theories with toric geometry.

On the BRST and finite field-dependent BRST of a model where vector and axial vector interactions get mixed up with different weights

The generalized version of a lower dimensional model where vector and axial vector interactions get mixed up with different weights is considered. The bosonized version of which does not possess the local gauge symmetry. An attempt has been made here to construct the BRST invariant reformulation of this model using Batalin–Fradlin and Vilkovisky formalism. It is found that the extra field needed to make it gauge invariant turns into Wess–Zumino scalar with appropriate choice of gauge fixing. An application of finite field-dependent BRST and anti-BRST transformation is also made here in order to show the transmutation between the BRST symmetric and the usual nonsymmetric version of the model.

Ward and Nielsen identities for ABJM theory in 𝒩 = 1 superspace

The structures and the associated gauge algebra of ABJM theory in [Formula: see text] superspace are reviewed. We derive the Ward identities of the theory in the class of Lorentz-type gauges at quantum level to justify the renormalizability of the model. We compute the Nielsen identities for the two-point functions of the theory with the help of enlarged BRST transformation. The identities are derived in ABJM theory to ensure the gauge independence of the physical poles of the Green’s functions.

Emergence of Lowenstein–Zimmermann mass terms for QED3

In this paper we consider a super-renormalizable theory of massless QED in (2 + 1) dimensions and discuss their BRST symmetry transformation. By extending the BRST transformation, we derive the Nielsen identities for the theory. Further, we compute the generalized BRST (so-called FFBRST) transformation by making the transformation parameter field dependent. Remarkably, we observe that the Lowenstein–Zimmermann mass terms, containing Lowenstein–Zimmermann parameter which plays an important role in the BPHZL renormalization program, along with the external sources coupled to the nonlinear BRST variations appear naturally in the theory through an FFBRST transformation.