Leading large order asymptotics for \((\phi ^ 4)_ 2\) perturbation theory
Let \(B(t)=\sum^{\infty}_{k=0}a_ kt^ k/k!\) for \(t\) in a disk of non-zero radius \(R\) be a representation of the Borel transform, \[ S(\phi)=\int_{\mathbb R^ 2}[(\nabla \phi)^ 2(x)+\phi^ 2(x)]\,d^ 2x- \ell n\int_{\mathbb R^ 2}\phi^ 4(x)\,d^ 2x \] where \(\phi \in W^{1,2}(\mathbb R^ 2)\). The main result of the paper is as follows: Let \(R\) be a radius of convergence of the Borel transform. Then \[ R^{-1}=\lim_{k\to \infty}| a_ k/k!|^{1/k}=\exp [-\inf_{\phi \in W^{1,2}(\mathbb R^ 2)}S(\phi)+2]. \]
large order perturbation theory asymptotics in quantum field theory
radius of convergence of the Borel transform
scientific article; zbMATH DE number 3907168
scientific article