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dc.contributor.author |
Friot, S. |
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dc.contributor.author |
Greynat, D. |
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dc.date.accessioned |
2019-02-09T19:28:19Z |
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dc.date.available |
2019-02-09T19:28:19Z |
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dc.date.issued |
2010 |
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dc.identifier.citation |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation / S. Friot, D. Greynat // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 15 назв. — англ. |
uk_UA |
dc.identifier.issn |
1815-0659 |
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dc.identifier.other |
2010 Mathematics Subject Classification: 41A60; 30E15 |
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dc.identifier.other |
DOI:10.3842/SIGMA.2010.079 |
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dc.identifier.uri |
http://dspace.nbuv.gov.ua/handle/123456789/146502 |
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dc.description.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 ''N-point'' functions for the simple case of zero-dimensional φ4 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. |
uk_UA |
dc.description.sponsorship |
We would like to thank Santi Peris and Eduardo de Rafael for their comments, as well as one of the referees for his suggestions to improve the manuscript. D.G. acknowledges financial support from CICYT-FEDER-FPA2008-01430, and the Spanish Consolider-Ingenio 2010 Program CPAN (CSD2007-00042). |
uk_UA |
dc.language.iso |
en |
uk_UA |
dc.publisher |
Інститут математики НАН України |
uk_UA |
dc.relation.ispartof |
Symmetry, Integrability and Geometry: Methods and Applications |
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dc.title |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
uk_UA |
dc.type |
Article |
uk_UA |
dc.status |
published earlier |
uk_UA |
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