Vanishing Cycles and Analysis of Singularities of Feynman Diagrams
In this work, we analyze the vanishing cycles of Feynman loop integrals by the means of the Mayer–Vietoris spectral sequence. A complete classification of possible vanishing geometries is obtained. We use this result for establishing an asymptotic expansion for the loop integrals near their singular...
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MDPI AG
2025-03-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/13/6/969 |
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| author | Stanislav Srednyak Vladimir Khachatryan |
| author_facet | Stanislav Srednyak Vladimir Khachatryan |
| author_sort | Stanislav Srednyak |
| collection | DOAJ |
| description | In this work, we analyze the vanishing cycles of Feynman loop integrals by the means of the Mayer–Vietoris spectral sequence. A complete classification of possible vanishing geometries is obtained. We use this result for establishing an asymptotic expansion for the loop integrals near their singularity locus and then give explicit formulas for the coefficients of such an expansion. Further development of this framework may potentially lead to exact calculations of one- and two-loop Feynman diagrams, as well as other next-to-leading and higher-order diagrams, in studies of radiative corrections for upcoming lepton–hadron scattering experiments. |
| format | Article |
| id | doaj-art-4ccf9dea02c64e45b72b5068aaffc063 |
| institution | OA Journals |
| issn | 2227-7390 |
| language | English |
| publishDate | 2025-03-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj-art-4ccf9dea02c64e45b72b5068aaffc0632025-08-20T01:48:41ZengMDPI AGMathematics2227-73902025-03-0113696910.3390/math13060969Vanishing Cycles and Analysis of Singularities of Feynman DiagramsStanislav Srednyak0Vladimir Khachatryan1Department of Physics, Duke University, Durham, NC 27708, USADepartment of Physics, Duke University, Durham, NC 27708, USAIn this work, we analyze the vanishing cycles of Feynman loop integrals by the means of the Mayer–Vietoris spectral sequence. A complete classification of possible vanishing geometries is obtained. We use this result for establishing an asymptotic expansion for the loop integrals near their singularity locus and then give explicit formulas for the coefficients of such an expansion. Further development of this framework may potentially lead to exact calculations of one- and two-loop Feynman diagrams, as well as other next-to-leading and higher-order diagrams, in studies of radiative corrections for upcoming lepton–hadron scattering experiments.https://www.mdpi.com/2227-7390/13/6/969algebraic geometryhomology classesMayer–Vietoris sequencepinch mapquantum electrodynamicsFeynman loop integrals |
| spellingShingle | Stanislav Srednyak Vladimir Khachatryan Vanishing Cycles and Analysis of Singularities of Feynman Diagrams Mathematics algebraic geometry homology classes Mayer–Vietoris sequence pinch map quantum electrodynamics Feynman loop integrals |
| title | Vanishing Cycles and Analysis of Singularities of Feynman Diagrams |
| title_full | Vanishing Cycles and Analysis of Singularities of Feynman Diagrams |
| title_fullStr | Vanishing Cycles and Analysis of Singularities of Feynman Diagrams |
| title_full_unstemmed | Vanishing Cycles and Analysis of Singularities of Feynman Diagrams |
| title_short | Vanishing Cycles and Analysis of Singularities of Feynman Diagrams |
| title_sort | vanishing cycles and analysis of singularities of feynman diagrams |
| topic | algebraic geometry homology classes Mayer–Vietoris sequence pinch map quantum electrodynamics Feynman loop integrals |
| url | https://www.mdpi.com/2227-7390/13/6/969 |
| work_keys_str_mv | AT stanislavsrednyak vanishingcyclesandanalysisofsingularitiesoffeynmandiagrams AT vladimirkhachatryan vanishingcyclesandanalysisofsingularitiesoffeynmandiagrams |