On the ambiguity of field correlators represented by asymptotic perturbation expansions

TL;DR

This paper investigates the ambiguity in reconstructing functions from divergent asymptotic perturbation series in Quantum Field Theory, using Borel-Laplace integrals and a modified Watson lemma, with implications for perturbative QCD.

Contribution

It introduces a modified Watson lemma to characterize functions sharing the same asymptotic series, highlighting the inherent ambiguity in perturbation expansions.

Findings

Identifies a large class of functions with identical asymptotic expansions.

Shows the ambiguity in function reconstruction from divergent series.

Discusses implications for perturbative QCD and the Adler function.

Abstract

Starting from the divergence pattern of perturbation expansions in Quantum Field Theory and the (assumed) asymptotic character of the series, we address the problem of ambiguity of a function determined by the perturbation expansion. We consider functions represented by an integral of the Laplace-Borel type along a general contour in the Borel complex plane. Proving a modified form of the Watson lemma, we obtain a large class of functions having the same asymptotic perturbation expansion. Some remarks on perturbative QCD are made, using the particular case of the Adler function.