Quark confinement and dynamical breakdown of chiral symmetry in covariant gauge QCD

Making only one widely accepted assumption that the full gluon propagator becomes infrared singular like (q2)-2 at small momenta, we investigate in a gauge-invariant way the Schwinger-Dyson equation for the quark propagator, completed by the corresponding Slavnov-Taylor identity. We find three and only three confinement-type solutions for the quark propagator in the infrared region. We also establish a close connection between quark confinement and chiral symmetry breaking. We discover that the ghost degrees of freedom play an essential role in the dynamics of chiral symmetry breaking, but, nevertheless, the infrared-finite (it does not depend on the infrared regulation parameter ε in the ε→0+ limit), gauge-invariant and nonperturbative quark propagator we obtained was free of ghost complications. (orig.)