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

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.

22 pages

References in corpus (6)

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• Dyson Schwinger Equations: From Hopf algebras to Number Theory
• Recursion and growth estimates in renormalizable quantum field theory
• Growth estimates for Dyson-Schwinger equations
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Cited by in corpus (18)

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• Resonant resurgent asymptotics from quantum field theory
• The core Hopf algebra
• Approximate Differential Equations for Renormalization Group Functions in Models Free of Vertex Divergencies
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Avoidance of a Landau Pole by Flat Contributions in QED
• Not so non-renormalizable gravity
• Algebraic Structures in local QFT
• Resurgent transseries $\&$ Dyson-Schwinger equations
• Hopf-algebraic Renormalization of QED in the linear covariant Gauge
• Next-to${}^k$ leading log expansions by chord diagrams
• Resurgence and self-completion in renormalized gauge theories
• Mulitgraded Dyson-Schwinger systems
• Feynman diagrams and their algebraic lattices
• Gluon Mass Generation from Renormalons and Resurgence
• Three Etudes in QFT