Gribov's equation for the Green function of light quarks

Abstract.

Gribov's scenario of supercritical charges in QCD is investigated. We perform a numerical study of the corresponding equation for the Green function of light quarks. This is done in an approximation which neglects all pion contributions. Different types of solutions in the Euclidean region are discussed and the mass function of the quark is calculated. The solutions of the equation are shown to have a qualitatively different behaviour if the strong coupling constant $\alpha_s$ exceeds a critical value $\alpha_c = 0.43$ in the infrared region. Chiral symmetry breaking is found to occur at supercritical coupling. The analytic structure of the solutions is investigated. Earlier results obtained by Gribov are confirmed and extended.