A new approach to resummation: Parametric Perturbation Theory

Abstract

We present a {\sl non--perturbative} method, called {\sl Parametric Perturbation Theory} (PPT), which is alternative to the ordinary perturbation theory. The method relies on a principle of simplicity for the observable solutions, which are constrained to be linear in a certain (unphysical) parameter. The perturbative expansion is carried out in this parameter and not in the physical coupling (as in ordinary perturbation theory). We show that the method is capable to resum the divergent perturbative series, to {\sl extract} the leading asymptotic (strong coupling) behavior and {\sl predict} with high accuracy the coefficients of the perturbative series.