%0 Journal Article
%T Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
%A Samuel Friot
%A David Greynat
%J Symmetry, Integrability and Geometry : Methods and Applications
%D 2010
%I National Academy of Science of Ukraine
%X Using a method mixing Mellin-Barnes representation and Borel resummation we show how to obtain hyperasymptotic expansions from the (divergent) formal power series which follow from the perturbative evaluation of arbitrary ''N-point'' functions for the simple case of zero-dimensional ¦Õ4 field theory. This hyperasymptotic improvement appears from an iterative procedure, based on inverse factorial expansions, and gives birth to interwoven non-perturbative partial sums whose coefficients are related to the perturbative ones by an interesting resurgence phenomenon. It is a non-perturbative improvement in the sense that, for some optimal truncations of the partial sums, the remainder at a given hyperasymptotic level is exponentially suppressed compared to the remainder at the preceding hyperasymptotic level. The Mellin-Barnes representation allows our results to be automatically valid for a wide range of the phase of the complex coupling constant, including Stokes lines. A numerical analysis is performed to emphasize the improved accuracy that this method allows to reach compared to the usual perturbative approach, and the importance of hyperasymptotic optimal truncation schemes.
%K exactly and quasi-exactly solvable models
%K Mellin-Barnes representation
%K hyperasymptotics
%K resurgence
%K non-perturbative effects
%K field theories in lower dimensions
%U http://dx.doi.org/10.3842/SIGMA.2010.079