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Эта публикация цитируется в 2 научных статьях (всего в 2 статьях)
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin–Barnes Representation
Samuel Friota, David Greynatb a Univ Paris-Sud, Institut de Physique Nucléaire, UMR 8608, Orsay, F-91405, France
b Institut de Física Altes Energies, Universitat Autònoma de Barcelona, E-08193 Bellaterra, Barcelona, Spain
Аннотация:
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 $\phi^4$ 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.
Ключевые слова:
exactly and quasi-exactly solvable models; Mellin–Barnes representation; hyperasymptotics; resurgence; non-perturbative effects; field theories in lower dimensions.
Поступила: 9 июня 2010 г.; в окончательном варианте 30 сентября 2010 г.; опубликована 7 октября 2010 г.
Образец цитирования:
Samuel Friot, David Greynat, “Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin–Barnes Representation”, SIGMA, 6 (2010), 079, 23 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma537 https://www.mathnet.ru/rus/sigma/v6/p79
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