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.
Categories: hep-th