Resurgent Analysis of Ward-Schwinger-Dyson Equations
Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we ensured that they possessed the properties of compatibility with the renormalisation group...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2021 |
| ISSN: | 1815-0659 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211348 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Resurgent Analysis of Ward-Schwinger-Dyson Equations. Marc P. Bellon and Enrico I. Russo. SIGMA 17 (2021), 075, 18 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862710158503706624 |
|---|---|
| author | Bellon, Marc P. Russo, Enrico I. |
| author_facet | Bellon, Marc P. Russo, Enrico I. |
| citation_txt | Resurgent Analysis of Ward-Schwinger-Dyson Equations. Marc P. Bellon and Enrico I. Russo. SIGMA 17 (2021), 075, 18 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we ensured that they possessed the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure known to allow for comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex are at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory.
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| first_indexed | 2026-03-19T11:29:49Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211348 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T11:29:49Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bellon, Marc P. Russo, Enrico I. 2025-12-30T15:53:29Z 2021 Resurgent Analysis of Ward-Schwinger-Dyson Equations. Marc P. Bellon and Enrico I. Russo. SIGMA 17 (2021), 075, 18 pages 1815-0659 2020 Mathematics Subject Classification: 81Q40; 81T16; 40G10 arXiv:2011.13822 https://nasplib.isofts.kiev.ua/handle/123456789/211348 https://doi.org/10.3842/SIGMA.2021.075 Building on our recent derivation of the Ward-Schwinger-Dyson equations for the cubic interaction model, we present here the first steps of their resurgent analysis. In our derivation of the WSD equations, we ensured that they possessed the properties of compatibility with the renormalisation group equations and independence from a regularisation procedure known to allow for comparable studies in the Wess-Zumino model. The interactions between the transseries terms for the anomalous dimensions of the field and the vertex are at the origin of unexpected features, for which the effect of higher order corrections is not precisely known at this stage: we are only at the beginning of the journey to use resurgent methods to decipher non-perturbative effects in quantum field theory. The authors feel indebted to Dirk Kreimer for his many inspirational works and find it befitting that this work be published in a special issue in his honour. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Resurgent Analysis of Ward-Schwinger-Dyson Equations Article published earlier |
| spellingShingle | Resurgent Analysis of Ward-Schwinger-Dyson Equations Bellon, Marc P. Russo, Enrico I. |
| title | Resurgent Analysis of Ward-Schwinger-Dyson Equations |
| title_full | Resurgent Analysis of Ward-Schwinger-Dyson Equations |
| title_fullStr | Resurgent Analysis of Ward-Schwinger-Dyson Equations |
| title_full_unstemmed | Resurgent Analysis of Ward-Schwinger-Dyson Equations |
| title_short | Resurgent Analysis of Ward-Schwinger-Dyson Equations |
| title_sort | resurgent analysis of ward-schwinger-dyson equations |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211348 |
| work_keys_str_mv | AT bellonmarcp resurgentanalysisofwardschwingerdysonequations AT russoenricoi resurgentanalysisofwardschwingerdysonequations |