The Gribov problem and its solution from a toy model point of view

Abstract

The standard Faddeev Popov gauge fixing procedure is put on solid grounds by taking into account a topological factor which corrects for the number of Gribov copies within the first Gribov horizon. Zwanziger's stochastic approach to gauge fixed Yang-Mills theory is briefly reviewed. A simple toy model is presented which illustrates both methods. Within the toy model, I show that a stochastic drift force can be constructed with which the gauged configurations are attracted by the fundamental modular region. The toy model shows that an action which gives rise to the drift force can be found. This makes a ``heat bath'' simulation possible, which is seen to be superior to the Langevin approach at the numerical level.