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

Abstract

Non-perturbative renormalization group approach to the dynamical chiral symmetry breaking is an effective method which can accommodate beyond the ladder (mean filed) approximation. The usual method relying on the 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 formulate a beyond the ladder equation and it gives almost gauge independent results for the chiral condensates.

25 pages, 7 figures

References in corpus (2)

• Exact evolution equation for the effective potential
• Fermion Interactions and Universal Behavior in Strongly Interacting Theories

Cited by in corpus (6)

• The nonperturbative functional renormalization group and its applications
• The QCD phase structure at finite temperature and density
• Non-Gaussian fixed points in fermionic field theories without auxiliary Bose-fields
• Higgs scalar potential coupled to gravity in the exponential parametrization in arbitrary gauge
• Functional renormalization group study of a four-fermion model with $CP$ violation
• QCD chiral phase diagram from weak functional renormalization group