Non-perturbative to perturbative QCD via the FFBRST

TL;DR

This paper introduces a finite field dependent BRST transformation to connect a new quadratic gauge in QCD, suggestive of abelian dominance, with the standard Lorenz gauge, enabling a transition from non-perturbative to perturbative regimes.

Contribution

It proposes a novel FFBRST transformation that relates a non-perturbative quadratic gauge to the perturbative Lorenz gauge in QCD, overcoming differences in BRST invariance.

Findings

Successfully constructed a field redefinition linking non-perturbative and perturbative QCD.

Demonstrated the transformation preserves gauge invariance despite differing BRST invariances.

Provided a method to analyze phases of QCD through gauge transformations.

Abstract

Recently a new type of quadratic gauge was introduced in QCD in which the degrees of freedom are suggestive of a phase of abelian dominance. In its simplest form it is also free of Gribov ambiguity. However this gauge is not suitable for usual perturbation theory. The finite field dependent BRST (FFBRST) transformation is a method established to interrelate generating functionals for different effective versions of gauge fixed field theories. In this paper we propose a FFBRST transformation suitable for transforming the theory in the new quadratic gauge into the standard Lorenz gauge Faddeev-Popov version of the effective lagrangian. The task is made interesting by the fact the BRST invariance obeyed by the two effective lagrangians are not the same, however suitable extension of the previous procedures accomplishes the required result. We are thus able to identify a field redefinition to go from a non-perturbative phase of QCD to perturbative QCD.