Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions
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arXiv
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| Hauptverfasser: | , , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915760979312640 |
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| author | Feng, Bo Li, Xiang Liu, Yuanche Ma, Yan-Qing Zhang, Yang |
| author_facet | Feng, Bo Li, Xiang Liu, Yuanche Ma, Yan-Qing Zhang, Yang |
| contents | We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield symbolic recurrence relations. We develop an efficient algorithm that utilizes these recurrences to reduce integrals to a minimal set of master integrals. This approach circumvents the exponential growth of traditional integration-by-parts relations, enabling the reduction of high-rank, multi-loop integrals critical for state-of-the-art calculations in perturbative quantum field theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_21769 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions Feng, Bo Li, Xiang Liu, Yuanche Ma, Yan-Qing Zhang, Yang High Energy Physics - Phenomenology High Energy Physics - Theory We introduce a novel, systematic method for the complete symbolic reduction of multi-loop Feynman integrals, leveraging the power of generating functions. The differential equations governing these generating functions naturally yield symbolic recurrence relations. We develop an efficient algorithm that utilizes these recurrences to reduce integrals to a minimal set of master integrals. This approach circumvents the exponential growth of traditional integration-by-parts relations, enabling the reduction of high-rank, multi-loop integrals critical for state-of-the-art calculations in perturbative quantum field theory. |
| title | Symbolic Reduction of Multi-loop Feynman Integrals via Generating Functions |
| topic | High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2509.21769 |