The Gribov problem and QCD dynamics

TL;DR

This paper reviews the Gribov problem in gauge fixing, the development of the GZ action as a non-perturbative tool for understanding confinement in QCD, and compares theoretical predictions with lattice data.

Contribution

It provides a pedagogic overview of Gribov's ideas, the GZ action, and their relation to confinement, including recent developments and comparisons with other approaches.

Findings

GZ action relates to confinement mechanisms

BRST symmetry breaking discussed in context

Comparison with lattice data supports GZ approach

Abstract

In 1967, Faddeev and Popov were able to quantize the Yang-Mills theory by introducing new particles called ghost through the introduction of a gauge. Ever since, this quantization has become a standard textbook item. Some years later, Gribov discovered that the gauge fixing was not complete, gauge copies called Gribov copies were still present and could affect the infrared region of quantities like the gauge dependent gluon and ghost propagator. This feature was often in literature related to confinement. Some years later, the semi-classical approach of Gribov was generalized to all orders and the so-called GZ action was born. Ever since, many related articles were published. This review tends to give a pedagogic review of the ideas of Gribov and the subsequent construction of the GZ action, including many other toipics related to the Gribov region. It is shown how the GZ action can be viewed as a non-perturbative tool which has relations with other approaches towards confinement. Many different features related to the GZ action shall be discussed in detail, such as BRST breaking, the KO criterion, the propagators, etc. We shall also compare with the lattice data and other non-perturbative approaches, including stochastic quantization.