Non-perturbative to perturbative QCD via the FFBRST

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.

BRST symmetry as a mechanism for confinement in the inter gauge framework

“…( 22) or (24) additionally gives an alternate approach to the passage between the effective actions of Lorenz and the quadratic gauges discussed in spirit in ref. [12]. This example proves for the first time that for a given passage between two theories, FFBRST transformation need not be lone.…”

“…Therefore, FFBRST may be useful to get an insight into phenomena in one theory given the knowledge of the same in the other theory. Hence, this technique finds numerous applications in interrelating two BRST invariant gauge fixed theories [2][3][4][5][6][7][8][9][10][11][12].…”

Compact space and infrared behavior of the effective QCD

“…The quadratic gauge has been extensively studied in various settings recently [10][11][12][13][14][15][16] and found to have substantial implications in non-perturbative sector of QCD. It is given as follows…”

Equivalence of two solutions of physical massive gravity

“…Over the period it has found various applications in field theory [23][24][25][26][27][28][29][30][31][32][33]. In a recent interesting work, the FFBRST technique itself has been extended to include connection of the theory with two different gauge fixings with a theory having only Lorenz gauge fixing [34]. [22].…”

“…Over the period it has found various applications in field theory [23][24][25][26][27][28][29][30][31][32][33]. In a recent interesting work, the FFBRST technique itself has been extended to include connection of the theory with two different gauge fixings with a theory having only Lorenz gauge fixing [34]. FFBRST transformation is a generalization of usual BRST transformation, with the infinitesimal global anti commuting parameter being replaced by a finite parameter dependent on fields.…”