Gribov ambiguities in non-Abelian gauge theories

Abstract: This thesis investigates the quantization of field theories using the functional integral formalism. Gauge invariance necessitates a gauge-fixing procedure that chooses a unique field configuration from each gauge orbit. Faddeev and Popov suggested an adjustment to the action that implements gauge fixing in this framework, however it has been found that this procedure fails to uniquely fix the gauge of non-Abelian gauge theories. This problem is known as the Gribov ambiguity. This thesis reproduces and discusses the work of Gribov, and it is illustrated how the Gribov horizons divide the functional space into regions Cn. Then, the Coulomb gauge of SU(2) is considered as an explicit example of Gribov ambiguities. The equation of the Gribov pendulum is derived, and the properties of its solutions are discussed. The thesis concludes with a short review of the consequences of the Gribov ambiguity, and of the possible restrictions to the integration range that have been proposed as a resolution to the problem.