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 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
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 |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | 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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| ISSN: | 1815-0659 |