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 $f(z)$ and a series $\ensuremath{\Sigma}{a}_{n}{z}^{n}$ by the requirement $|f(z)\ensuremath{-}\ensuremath{\Sigma}\stackrel{N}{n=0}{a}_{n}{z}^{n}|<~A{\ensuremath{\sigma}}^{N+1}(N+1)!{|z|}^{N+1}$ is applicable to certain divergent series.

Locations

• Physical Review Letters - View
• CaltechAUTHORS (California Institute of Technology) - View - PDF