Numerators in Parametric Representations of Feynman Diagrams
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866909478830473216 |
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| author | Bellon, Marc P. |
| author_facet | Bellon, Marc P. |
| contents | The parametric representation has been used since 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 ground work 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 to a vacuum graph allows for a strong reduction of the maximal power of the Symanzik polynomial in the denominator. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_05028 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Numerators in Parametric Representations of Feynman Diagrams Bellon, Marc P. High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics 81T18, 81Q30, 15A15 The parametric representation has been used since 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 ground work 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 to a vacuum graph allows for a strong reduction of the maximal power of the Symanzik polynomial in the denominator. |
| title | Numerators in Parametric Representations of Feynman Diagrams |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory Mathematical Physics 81T18, 81Q30, 15A15 |
| url | https://arxiv.org/abs/2207.05028 |