Wilson Renormalization Group Equations for the Critical Dynamics of Chiral Symmetry

TL;DR

This paper develops Wilson renormalization group equations to analyze the critical dynamics of chiral symmetry breaking, comparing results with the Schwinger-Dyson approach and deriving key critical parameters.

Contribution

It derives beta functions for four-fermi couplings within the Wilson RG framework, linking critical behavior to Schwinger-Dyson results under specific approximations.

Findings

Beta functions for four-fermi couplings obtained

Critical couplings and anomalous dimensions calculated

Critical behavior consistent with Schwinger-Dyson analysis

Abstract

The critical dynamics of the chiral symmetry breaking induced by gauge interaction is examined in the Wilson renormalization group framework in comparison with the Schwinger-Dyson approach. We derive the beta functions for the four-fermi couplings in the sharp cutoff renormalzation group scheme, from which the critical couplings and the anomalous dimensions of the fermion composite operators near criticality are immediately obtained. It is also shown that the beta functions lead to the same critical behavior found by solving the so-called ladder Schwinger-Dyson equation, if we restrict the radiative corrections to a certain limited type.