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

Abstract

Clarification of the presentation of results. Equations and results unchanged. Match the published version. 12 pages.International audienceI 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