Intersection theory, relative cohomology and the Feynman parametrization
Abstract We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction c...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2025-05-01
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| Series: | Journal of High Energy Physics |
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| Online Access: | https://doi.org/10.1007/JHEP05(2025)158 |
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| _version_ | 1849470132211941376 |
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| author | Mingming Lu Ziwen Wang Li Lin Yang |
| author_facet | Mingming Lu Ziwen Wang Li Lin Yang |
| author_sort | Mingming Lu |
| collection | DOAJ |
| description | Abstract We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction can then be achieved by computing intersection numbers. We apply our method in several examples to demonstrate its correctness, and discuss the subtleties in certain degenerate limits. |
| format | Article |
| id | doaj-art-f6e8fa42c13a435ab8bd3a53c8484ddb |
| institution | Kabale University |
| issn | 1029-8479 |
| language | English |
| publishDate | 2025-05-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of High Energy Physics |
| spelling | doaj-art-f6e8fa42c13a435ab8bd3a53c8484ddb2025-08-20T03:25:15ZengSpringerOpenJournal of High Energy Physics1029-84792025-05-012025512310.1007/JHEP05(2025)158Intersection theory, relative cohomology and the Feynman parametrizationMingming Lu0Ziwen Wang1Li Lin Yang2Zhejiang Institute of Modern Physics, School of Physics, Zhejiang UniversityZhejiang Institute of Modern Physics, School of Physics, Zhejiang UniversityZhejiang Institute of Modern Physics, School of Physics, Zhejiang UniversityAbstract We present a novel approach for loop integral reduction in the Feynman parametrization using intersection theory and relative cohomology. In this framework, Feynman integrals correspond to boundary-supported differential forms in the language of relative cohomology. The integral reduction can then be achieved by computing intersection numbers. We apply our method in several examples to demonstrate its correctness, and discuss the subtleties in certain degenerate limits.https://doi.org/10.1007/JHEP05(2025)158Differential and Algebraic GeometryScattering Amplitudes |
| spellingShingle | Mingming Lu Ziwen Wang Li Lin Yang Intersection theory, relative cohomology and the Feynman parametrization Journal of High Energy Physics Differential and Algebraic Geometry Scattering Amplitudes |
| title | Intersection theory, relative cohomology and the Feynman parametrization |
| title_full | Intersection theory, relative cohomology and the Feynman parametrization |
| title_fullStr | Intersection theory, relative cohomology and the Feynman parametrization |
| title_full_unstemmed | Intersection theory, relative cohomology and the Feynman parametrization |
| title_short | Intersection theory, relative cohomology and the Feynman parametrization |
| title_sort | intersection theory relative cohomology and the feynman parametrization |
| topic | Differential and Algebraic Geometry Scattering Amplitudes |
| url | https://doi.org/10.1007/JHEP05(2025)158 |
| work_keys_str_mv | AT mingminglu intersectiontheoryrelativecohomologyandthefeynmanparametrization AT ziwenwang intersectiontheoryrelativecohomologyandthefeynmanparametrization AT lilinyang intersectiontheoryrelativecohomologyandthefeynmanparametrization |