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

TL;DR

This paper analyzes the structure of QED beta functions using Dyson-Schwinger equations, revealing conditions for Landau poles and solution behaviors beyond perturbation theory.

Contribution

It introduces a novel approach to study beta functions via Dyson-Schwinger equations as differential equations, clarifying Landau pole existence beyond perturbation theory.

Findings

Conditions for the existence of Landau poles are explicitly characterized.

The structure of beta functions is linked to the asymptotics of skeleton graphs.

A new method for analyzing Dyson-Schwinger equations as ODEs is proposed.

Abstract

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.