Chiral symmetry breakdown. I. Gauge dependence in constant vertex approximation

Abstract

An approximate quark propagator equation in a Landau-like gauge is analyzed and it is shown that there is a critical value of the coupling constant, corresponding to the onset of dynamical chiral symmetry breakdown, provided that (a) there is an infrared cutoff, which can be supplied by an effective gluon mass, and (b) there is an ultraviolet cutoff, which may be engendered by a running coupling constant. Dynamical chiral symmetry breakdown is shown not to occur in other gauges under the same circumstances, thus casting doubt upon the approximations commonly used.