The QED beta-function from global solutions to Dyson-Schwinger equations

Understand

We discuss the structure of beta functions as determined by the recursive nature of Dyson--Schwinger equations turned into an analysis of ordinary differential equations, with particular emphasis given to quantum electrodynamics.

• In particular we determine when a separatrix for solutions to such ODEs exists and clarify the existence of Landau poles beyond perturbation theory.
• Both are determined in terms of explicit conditions on the asymptotics for the growth of skeleton graphs.