Recursion and growth estimates in renormalizable quantum field theory

Abstract

In this paper we show that there is a Lipatov bound for the radius of convergence for superficially divergent one-particle irreducible Green functions in a renormalizable quantum field theory if there is such a bound for the superficially convergent ones. The radius of convergence turns out to be $\min \{\rho ,1/b_1\}$, where $\rho$ is the bound on the convergent ones, the instanton radius, and $b_1$ the first coefficient of the $\beta$-function.

21 pages

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• The QCD beta-function from global solutions to Dyson-Schwinger equations
• Growth estimates for Dyson-Schwinger equations
• The core Hopf algebra
• Semiclassical Trans-Series from the Perturbative Hopf-Algebraic Dyson-Schwinger Equations: ${\varphi }^3$ QFT in 6 Dimensions
• Some combinatorial aspects of quantum field theory
• Not so non-renormalizable gravity
• Log-Expansions from Combinatorial Dyson-Schwinger Equations
• The next-to-ladder approximation for Dyson-Schwinger equations
• Resurgence and self-completion in renormalized gauge theories
• Algebra for quantum fields
• Ladders and rainbows in Minimal Subtraction
• Gluon Mass Generation from Renormalons and Resurgence
• Uncovering Hidden Patterns: Approximate Resurgent Resummation from Truncated Series
• Riemann-Hilbert Problem and Quantum Field Theory: Integrable Renormalization, Dyson-Schwinger Equations
• A mathematical perspective on the phenomenology of non-perturbative Quantum Field Theory