Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies

TL;DR

The paper presents an approximation method to derive differential equations for the renormalization group beta function from Schwinger-Dyson equations, effectively capturing dominant asymptotic behavior in models without vertex divergences.

Contribution

It introduces a new approximation scheme linking Schwinger-Dyson equations to RG functions, applicable to models lacking vertex divergences, simplifying quantum correction analysis.

Findings

Captures dominant asymptotic behavior of perturbative solutions.

Effective in models without divergent vertex functions.

Provides a practical approach for RG analysis in specific models.

Abstract

I introduce an approximation scheme that allows to deduce differential equations for the renormalization group $\beta$-function from a Schwinger--Dyson equation for the propagator. This approximation is proven to give the dominant asymptotic behavior of the perturbative solution. In the supersymmetric Wess--Zumino model and a $\phi^3_6$ scalar model which do not have divergent vertex functions, this simple Schwinger--Dyson equation for the propagator captures the main quantum corrections.