Solving the QCD non-perturbative flow equation as a partial differential equation and its application to dynamical chiral symmetry breaking

Abstract

The non-perturbative renormalization group approach to dynamical chiral symmetry breaking is an effective method which can accommodate beyond the ladder (mean field) approximation. The usual method relying on field operator expansion suffers explosive behaviors of the 4-fermi coupling constant, which prevent us from evaluating the physical quantities in the broken phase. In order to overcome this difficulty, we solve the flow equation directly as a partial differential equation and calculate the dynamical mass and the chiral condensates. Also, we go beyond the ladder approximation to formulate an equation which gives almost gauge-independent results for the chiral condensates. © 2013 The Author(s).