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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.
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Contributor : Sophie Heurteau Connect in order to contact the contributor
Submitted on : Monday, November 8, 2010 - 11:07:49 AM
Last modification on : Wednesday, September 16, 2020 - 4:08:13 PM

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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⟩



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