NONPERTURBATIVE QUARK PROPAGATOR APPROACH TO QCD AT LARGE DISTANCES

Abstract

A nonperturbative approach to QCD at large distances in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identity in the quark sector is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singular like (q2)−2 in the arbitrary covariant gauge, we find three and only three confinement-type solutions for the quark propagator (quark confinement theorem). Two of them vanish after the removal of the infrared regulation parameter. The third solution does not depend on this latter parameter, but it has no pole and it implies dynamical chiral symmetry breakdown (DCSB), which means a close connection between quark confinement and DCSB. We also show that multiplication solely by the quark infrared renormalization constant would make all the Green’s functions infrared finite (multiplicative renormalizability). The final forms of the renormalized (infrared finite) quark SD equations do not explicitly depend on a gauge-fixing parameter (“gauge invariance”). Our approach is free of ghost complications despite the fact that they play an essential role in nonperturbative dynamics. Our approach also implies the existence of a characteristic scale at which confinement, DCSB and other nonperturbative effects become essential. We solve explicitly the SD equation with corresponding ST identity for the above-mentioned IR finite quark propagator in the chiral limit and apply an effective potential in order to determine completely this solution.