Leading large order asymptotics for \((\phi ^ 4)_ 2\) perturbation theory. (English) Zbl 0568.46055

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 \[ R^{-1}=\lim_{k\to \infty}| a_ k/k!|^{1/k}=\exp [-\inf_{\phi \in W^{1,2}(\mathbb R^ 2)}S(\phi)+2]. \]
Reviewer: Yu. V. Kostarchuk


81T08 Constructive quantum field theory
46N50 Applications of functional analysis in quantum physics
81Q15 Perturbation theories for operators and differential equations in quantum theory
41A50 Best approximation, Chebyshev systems
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