Summability Methods, the Strong Asymptotic Condition, and Unitarity in Quantum Field Theory

Abstract

We discuss a summability mechanism which preserves nonlinear perturbative conditions such as unitarity of the Feynman series. This condition, which relates a function $f\left(z\right)\mathrm{}$ and a series $\Sigma a_n{z}^n$ by the requirement $\mathrm{}\left|f\right(z)-\Sigma \stackrel{N}{n=0\mathrm{}}{a}_n{z}^n|<~A{\sigma }^{N+1\mathrm{}}\mathrm{}(N+1\mathrm{})!{\mathrm{}\left|z\right|\mathrm{}}^{N+1\mathrm{}}$ is applicable to certain divergent series.