Gribov's ambiguities and horizons

Gribov's ambiguities prevent a formulation of a gauge theory on the whole space of field configurations. We introduce the concept of horizon around some field $A^0$ as the nearest field to it exhibiting gauge ambiguities. The constrained equations determining the horizon are explicitly given. These concepts are applied to the gauge problems associated with collective coordinates. For a two-dimensional model, horizon solutions around one soliton are found for a whole family of gauges and its properties are analyzed. By varying the gauge condition we show that the "optimal horizon," the one which surrounds the largest portion of functional space, lies at the threshold of soliton-antisoliton production.