Abstract
A gauge-invariant, nonperturbative approach to quark confinement and chiral-symmetry breaking in the context of the Schwinger-Dyson equations and corresponding Slavnov-Taylor identities is presented. Making only one widely accepted assumption that the full gluon propagator becomes an infrared singularity like {ital q}{sup {minus}4} at small momenta, we obtain a nonperturbative, gauge-invariant, infrared-finite quark propagator, which has no pole (confinement-type solution) and implies chiral-symmetry breaking (dynamical quark mass generation), so that we establish a close connection between these nonperturbative phenomena. We discover that the ghost degrees of freedom play an essential role in the dynamics of chiral-symmetry breaking, but nevertheless the quark propagator we got was free of ghost complications. In addition to the infrared-finite solution, we find also two infrared-vanishing (after the removal of the infrared regulation parameter) solutions for the quark propagator. For the dynamical (nonperturbative) quark mass we derive the expression which exhibits an essential singularity in the coupling constant in accordance with renormalization-group solutions in the infrared region.
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