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 that the effective lagrangian is invariant under two different BRST transformations which leads to suitable extension of the previous procedures to accomplish the required result. We are thus able to identify a field redefinition to go from a non-perturbative phase of QCD to perturbative QCD.
Highlights
Extensions of the usual Lorenz gauge by including the order terms quadratic in gauge fields have been studied in several contexts [1,2,3,4,5,6]
The vacuum in the quadratic gauge is provided by the SU (N ) symmetric ghost condensation of bilinears [7,8] which is non perturbative in nature since the non perturbative confining phase corresponds to this vacuum [7,8] and it arises at Lagrangian level only as is clear from Eq (4)
Such a vacuum does not exist in the theory of Lorenz gauge
Summary
Extensions of the usual Lorenz gauge by including the order terms quadratic in gauge fields have been studied in several contexts [1,2,3,4,5,6]. The vacuum in the quadratic gauge is provided by the SU (N ) symmetric ghost condensation of bilinears [7,8] which is non perturbative in nature since the non perturbative confining phase corresponds to this vacuum [7,8] and it arises at Lagrangian level only as is clear from Eq (4). Such a vacuum does not exist in the theory of Lorenz gauge. This conclusion is not at all surprising as the FFBRST is designed to connect two theories and not the quantities derivable from the theory regardless of the fact that theories belong to the same or two different vacua
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
