Skip to Main content Skip to Navigation
Journal articles

Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin–Barnes Representation

Abstract : 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 " -point" functions for the simple case of zero-dimensional 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.
Document type :
Journal articles
Complete list of metadatas

http://hal.in2p3.fr/in2p3-00533698
Contributor : Sophie Heurteau <>
Submitted on : Monday, November 8, 2010 - 11:07:49 AM
Last modification on : Wednesday, September 16, 2020 - 4:08:13 PM

Links full text

Identifiers

Collections

Citation

S. Friot, D. Greynat. Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin–Barnes Representation. Symmetry, Integrability and Geometry : Methods and Applications, National Academy of Science of Ukraine, 2010, 6, pp.079. ⟨10.3842/SIGMA.2010.079⟩. ⟨in2p3-00533698⟩

Share

Metrics

Record views

125