Uniqueness and Significance of Weak Solution of Non-perturbative Renormalization Group Equation to Analyze Dynamical Chiral Symmetry Breaking

TL;DR

This paper introduces a novel method using weak solutions of non-perturbative renormalization group equations to analyze dynamical chiral symmetry breaking, accurately predicting physical quantities even in complex phase transitions.

Contribution

It develops a new mathematical approach to solve RG equations with singularities, enabling precise analysis of chiral symmetry breaking in gauge theories.

Findings

Successfully predicts chiral condensates and dynamical mass.

Effectively handles first order phase transitions in finite density QCD.

Provides a mathematically rigorous framework for non-perturbative analysis.

Abstract

We propose quite a new method of analyzing the dynamical chiral symmetry breaking in gauge theories. Starting with the non-perturbative renormalization group equation for the Wilsonian fermion potential, we define the weak solution of it in order to mathematically authorize solutions with singularity. The weak solution is obtained uniquely and it successfully predicts the physically correct vacuum, chiral condensates, dynamical mass, through its auto-convexizing power for the effective potential. Thus it works perfectly even for the first order phase transition in the finite density QCD.