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

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 ${\varphi }_6^3$ scalar model which do not have divergent vertex functions, this simple Schwinger--Dyson equation for the propagator captures the main quantum corrections.

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

References in corpus (7)

• An Étude in non-linear Dyson--Schwinger Equations
• Recursive relations in the core Hopf algebra
• Renormalization group functions for the Wess-Zumino model: up to 200 loops through Hopf algebras
• The QCD beta-function from global solutions to Dyson-Schwinger equations
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Cited by in corpus (10)

• An Efficient Method for the Solution of Schwinger--Dyson equations for propagators
• A Schwinger--Dyson Equation in the Borel Plane: singularities of the solution
• Remarks on a melonic field theory with cubic interaction
• Dyson-Schwinger Equations in Minimal Subtraction
• Ward-Schwinger-Dyson equations in ${\varphi }_6^3$ Quantum Field Theory
• Higher loop corrections to a Schwinger--Dyson equation
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Resurgent Analysis of Ward-Schwinger-Dyson Equations
• Algebra for quantum fields
• Ladders and rainbows in Minimal Subtraction