Infrared structure of two-dimensional covariant gauge QCD

A nonperturbative approach to 2D covariant gauge QCD is presented in the context of the Schwinger–Dyson equations for the quark and ghost propagators and the corresponding Slavnov–Taylor identity. The distribution theory, complemented by the dimensional regularization method, is used in order to correctly treat the infrared singularities which inevitably appear in the theory. By working out the multiplicative renormalization program we remove them from the theory on a general ground and in a self-consistent way. This makes it possible to sum up the infinite series of the corresponding planar skeleton diagrams in order to derive a closed set of equations for the infrared renormalized quark propagator. We have shown that complications due to ghost degrees of freedom can be considerable within our approach. It is shown exactly that 2D covariant gauge QCD implies quark confinement (the quark propagator has no poles, indeed) as well as dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden).