Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation
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-dimensio...
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| Дата: | 2010 |
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| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2010
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146502 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1465022019-02-10T01:24:58Z Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation Friot, S. Greynat, D. 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. 2010 Article 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 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| 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. |
| format |
Article |
| author |
Friot, S. Greynat, D. |
| spellingShingle |
Friot, S. Greynat, D. Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Friot, S. Greynat, D. |
| author_sort |
Friot, S. |
| title |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
| title_short |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
| title_full |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
| title_fullStr |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
| title_full_unstemmed |
Non-Perturbative Asymptotic Improvement of Perturbation Theory and Mellin-Barnes Representation |
| title_sort |
non-perturbative asymptotic improvement of perturbation theory and mellin-barnes representation |
| publisher |
Інститут математики НАН України |
| publishDate |
2010 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/146502 |
| citation_txt |
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. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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2023-05-20T17:24:57Z |
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2023-05-20T17:24:57Z |
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