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

We discuss a summability mechanism which preserves nonlinear perturbative conditions such as unitarity of the Feynman series. This condition, which relates a function f(z) and a series a_nzⁿ by the requirement |f(z)- n=0Na_nzⁿ|<=Aσ^N+1(N+1)!|z|^N+1 is applicable to certain divergent series.