Quantizing SU(N) gauge theories without gauge fixing

TL;DR

This paper presents a gauge-invariant quantization method for SU(N) gauge theories that avoids gauge fixing and the Gribov problem, demonstrating perturbative equivalence to Landau gauge and deriving a gluon mass estimate consistent with QCD sum rules.

Contribution

It extends a gauge-invariant quantization procedure to non-Abelian SU(N) theories, clarifying the perturbative impact of the Gribov problem and relating gluon mass to the gluon condensate.

Findings

Perturbative equivalence to Landau gauge fixing.

Gluon mass estimate consistent with QCD sum rules.

Avoidance of the Gribov problem at the non-perturbative level.

Abstract

We generalize and extend a quantization procedure proposed by the present authors which is designed to quantize SU(N) gauge theories in the continuum without fixing the gauge and thereby avoid the Gribov problem. In particular we discuss the BRS symmetry underlying the effective action. We proceed to use this BRS symmetry to discuss the perturbative renormalization of the theory and show that perturbatively the procedure is equivalent to Landau gauge fixing. This generalizes earlier results obtained in the Abelian case to the non-abelian case and confirms the widely held believe that the Gribov problem manifests itself on the non-perturbative level, while not affecting the perturbative results. A relation between the gluon mass and gluon condensate in QCD is obtained which yields a gluon mass consistent with other estimates for values of the gluon condensate obtained from QCD sum rules.