Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
Vernadsky National Library of Ukraine
Переглянути архів Інформація| Поле | Співвідношення | |
| Title |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
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| Creator |
Friot, S.
Greynat, D. |
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| Description |
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.
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| Date |
2019-02-09T19:28:19Z
2019-02-09T19:28:19Z 2010 |
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| Type |
Article
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| Identifier |
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.
1815-0659 2010 Mathematics Subject Classification: 41A60; 30E15 DOI:10.3842/SIGMA.2010.079 http://dspace.nbuv.gov.ua/handle/123456789/146502 |
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| Language |
en
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| Relation |
Symmetry, Integrability and Geometry: Methods and Applications
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| Publisher |
Інститут математики НАН України
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