Analysis of the Wilsonian Effective Potentials in Dynamical Chiral Symmetry Breaking

TL;DR

This paper uses a non-perturbative renormalization group approach to analyze dynamical chiral symmetry breaking, showing the effective potential's non-analyticity and its relation to fermion mass generation.

Contribution

It introduces a simple approximation scheme for the Wilsonian effective potential and connects the renormalization group method with the Schwinger-Dyson equation for fermion mass.

Findings

Effective potential becomes non-analytic in infrared.

RG equation yields the same fermion mass as Schwinger-Dyson equation.

Introducing collective fields aids in evaluating order parameters.

Abstract

The non-perturbative renormalization group equation for the Wilsonian effective potential is given in a certain simple approximation scheme in order to study chiral symmetry breaking phenomena dynamically induced by strong gauge interactions. The evolving effective potential is found to be non-analytic in infrared, which indicates spontaneous generation of the fermion mass. It is also shown that the renormalization group equation gives the identical effective fermion mass with that obtained by solving the Schwinger-Dyson equation in the (improved) ladder approximation. Moreover introduction of the collective field corresponding to the fermion composite into the theory space is found to offer an efficient method to evaluate the order parameters; the dynamical mass and the chiral condensate. The relation between the renormalization group equation incorporating the collective field and the Schwinger-Dyson equation is also clarified.