Recursion and growth estimates in renormalizable quantum field theory

Details Recursion and growth estimates in renormalizable quantum field theory Recursion and growth estimates in renormalizable quantum field theory

2006-12-18

arxiv.org/abs/hep-th/0612179v1

Commun.Math.Phys.279:401-427,2008

Physics

High Energy Physics

High Energy Physics - Theory

21 pages

Scientific paper

10.1007/s00220-008-0431-7

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 ${\rm min}\{\rho,1/b_1\}$, where $\rho$ is the bound on the convergent ones, the instanton radius, and $b_1$ the first coefficient of the $\beta$-function.

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