I. The mass gap and solution of the quark confinement problem in QCD

Abstract

Using the previously derived confining gluon propagator, the corresponding system of equations determining the quark propagator is derived. The system of equations consists of the Schwinger-Dyson equation for the quark propagator itself, which includes the zero momentum transfer quark-gluon vertex. It is complemented by the Slavnov-Taylor identity for this vertex. The quark equation depends explicitly on the mass gap, determining the scale of the truly nonperturbative dynamics in the QCD ground state. The obtained system of equations is manifestly gauge-invariant, i.e., does not depend explicitly on the gauge-fixing parameter. It is also free from all the types of the perturbative contributions ("contaminations"), which may appear at the fundamental quark-gluon level.