Particular solutions of the equations for the lowest Green's functions in the infrared region of quantum chromodynamics

Solutions of the Schwinger–Dyson equations for the ghost and quark propagators in QCD are investigated in the infrared region. A gauge is shown to exist in which the equation for the ghost propagator possesses a free solution. This result is used to substantiate the possibility of the ghost contribution removal from the gauge identity for the quark-gluon vertex in this particular gauge. A new class of solutions of the equation for the quark propagator is obtained under these conditions. This class includes solutions with broken chiral invariance which are non-analytical in the coupling constant.