Numerators in Parametric Representations of Feynman Diagrams
The parametric representation has been used for a long time for the evaluation of Feynman diagrams. As a dimension-independent intermediate representation, it allows a clear description of singularities. Recently, it has become a choice tool for the investigation of the type of transcendent numbersa...
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2025 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут математики НАН України
2025
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212884 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Numerators in Parametric Representations of Feynman Diagrams. Marc P. Bellon. SIGMA 21 (2025), 007, 25 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862573415364296704 |
|---|---|
| author | Bellon, Marc P. |
| author_facet | Bellon, Marc P. |
| citation_txt | Numerators in Parametric Representations of Feynman Diagrams. Marc P. Bellon. SIGMA 21 (2025), 007, 25 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The parametric representation has been used for a long time for the evaluation of Feynman diagrams. As a dimension-independent intermediate representation, it allows a clear description of singularities. Recently, it has become a choice tool for the investigation of the type of transcendent numbersappearing in the evaluation of Feynman diagrams. The inclusion of numerators has, however, stagnated since the groundwork of Nakanishi. I here show howto greatly simplify the formulas through the use of Dodgson identities. In the massless case in particular, reduction to the completion of a vacuum graph allows for a strong reduction of the maximal power of the Symanzik polynomial in the denominator.
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| first_indexed | 2026-03-21T11:38:32Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212884 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-21T11:38:32Z |
| publishDate | 2025 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Bellon, Marc P. 2026-02-13T13:50:38Z 2025 Numerators in Parametric Representations of Feynman Diagrams. Marc P. Bellon. SIGMA 21 (2025), 007, 25 pages 1815-0659 2020 Mathematics Subject Classification: 81T18; 81Q30; 15A15 arXiv:2207.05028 https://nasplib.isofts.kiev.ua/handle/123456789/212884 https://doi.org/10.3842/SIGMA.2025.007 The parametric representation has been used for a long time for the evaluation of Feynman diagrams. As a dimension-independent intermediate representation, it allows a clear description of singularities. Recently, it has become a choice tool for the investigation of the type of transcendent numbersappearing in the evaluation of Feynman diagrams. The inclusion of numerators has, however, stagnated since the groundwork of Nakanishi. I here show howto greatly simplify the formulas through the use of Dodgson identities. In the massless case in particular, reduction to the completion of a vacuum graph allows for a strong reduction of the maximal power of the Symanzik polynomial in the denominator. I would like to thank the anonymous referees for their criticisms and suggestions. They addressed serious shortcomings in previous versions of this work to make it more readable, both in terms of the precise results established and the way they can be derived. Any remaining difficulties are nevertheless of my entire responsibility. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Numerators in Parametric Representations of Feynman Diagrams Article published earlier |
| spellingShingle | Numerators in Parametric Representations of Feynman Diagrams Bellon, Marc P. |
| title | Numerators in Parametric Representations of Feynman Diagrams |
| title_full | Numerators in Parametric Representations of Feynman Diagrams |
| title_fullStr | Numerators in Parametric Representations of Feynman Diagrams |
| title_full_unstemmed | Numerators in Parametric Representations of Feynman Diagrams |
| title_short | Numerators in Parametric Representations of Feynman Diagrams |
| title_sort | numerators in parametric representations of feynman diagrams |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212884 |
| work_keys_str_mv | AT bellonmarcp numeratorsinparametricrepresentationsoffeynmandiagrams |