Chiral Symmetry Breaking in Axial Gauge QCD from the Dyson Schwinger Equations

Abstract

We investigate the nonperturbative behaviour of the quark propagator in axial gauge using a truncation of the Dyson-Schwinger equations which respects the Ward-Takahashi identity and multiplicative renormalisability. We demonstrate that above a critical coupling $\alpha_c$, which depends on the form of the gluon propagator, one can obtain massive solutions for both explicit and dynamically generated quark masses. The stability of these is discussed in the context of the Cornwall-Jackiw-Tomboulis effective action.