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

References in corpus (1)

• The next-to-ladder approximation for Dyson-Schwinger equations

Cited by in corpus (2)

• Growth estimates for Dyson-Schwinger equations
• The next-to-ladder approximation for Dyson-Schwinger equations