Two-dimensional QCD in the covariant gauge

Abstract

A nonperturbative approach to two-dimensional covariant gauge QCD is presented in the context of the Schwinger-Dyson equations and the corresponding Slavnov-Taylor identities. The distribution theory, complemented by the dimensional regularization method, is used in order to treat correctly the infrared singularities which inevitably appear in the theory. By working out the multiplicative renormalization program, we remove them from the theory on general grounds and in a self-consistent way, proving thus the infrared multiplicative renormalizability of two-dimensional QCD within our approach. 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 the dynamical breakdown of chiral symmetry (a chiral symmetry preserving solution is forbidden). We also show explicitly how to formulate the bound-state problem and the Schwinger-Dyson equations for the gluon propagator and the triple gauge field proper vertex, all free from the severe infrared singularities.