## 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

### MSC:

 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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### References:

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