Gauge-fixing degeneracies and confinement in non-Abelian gauge theories

Abstract

Following several suggestions of Gribov we have examined the problem of gauge-fixing degeneracies in non-Abelian gauge theories. First we modify the usual Faddeev-Popov prescription to take gauge-fixing degeneracies into account. We obtain a formal expression for the generating functional which is invariant under finite gauge transformations and which counts gauge-equivalent orbits only once. Next we examine the instantaneous Coulomb interaction in the canonical formalism with the Coulomb-gauge condition. We find that the spectrum of the Coulomb Green's function in an external monopole-like field configuration has an accumulation of negative-energy bound states at $E=0$. Using semiclassical methods we show that this accumulation phenomenon, which is closely linked with gauge-fixing degeneracies, modifies the usual Coulomb propagator from ${|\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}|}^{\ensuremath{-}2}$ to ${|\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}|}^{\ensuremath{-}4}$ for small $|\stackrel{\ensuremath{\rightarrow}}{\mathrm{k}}|$. This confinement behavior depends only on the long-range behavior of the field configuration. We thereby demonstrate the conjectured confinement property of non-Abelian gauge theories in the Coulomb gauge.