New Techniques for Worldline Integration
The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining th...
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| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
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| Дата: | 2021 |
| Автори: | , , , |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2021
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| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/211358 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | New Techniques for Worldline Integration. James P. Edwards, C. Moctezuma Mata, Uwe Müller and Christian Schubert. SIGMA 17 (2021), 065, 19 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862685040416129024 |
|---|---|
| author | Edwards, James P. Mata, C. Moctezuma Müller, Uwe Schubert, Christian |
| author_facet | Edwards, James P. Mata, C. Moctezuma Müller, Uwe Schubert, Christian |
| citation_txt | New Techniques for Worldline Integration. James P. Edwards, C. Moctezuma Mata, Uwe Müller and Christian Schubert. SIGMA 17 (2021), 065, 19 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining the contributions of large classes of Feynman diagrams of different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding to individual diagrams poses a formidable mathematical challenge. We summarize the history and state of the art of this problem, including some natural connections to the theory of Bernoulli numbers and polynomials and multiple zeta values.
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| first_indexed | 2026-03-17T11:03:47Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211358 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-17T11:03:47Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Edwards, James P. Mata, C. Moctezuma Müller, Uwe Schubert, Christian 2025-12-30T15:55:16Z 2021 New Techniques for Worldline Integration. James P. Edwards, C. Moctezuma Mata, Uwe Müller and Christian Schubert. SIGMA 17 (2021), 065, 19 pages 1815-0659 2020 Mathematics Subject Classification: 11B68; 33C65; 81Q30 arXiv:2106.12071 https://nasplib.isofts.kiev.ua/handle/123456789/211358 https://doi.org/10.3842/SIGMA.2021.065 The worldline formalism provides an alternative to Feynman diagrams in the construction of amplitudes and effective actions that shares some of the superior properties of the organization of amplitudes in string theory. In particular, it allows one to write down integral representations combining the contributions of large classes of Feynman diagrams of different topologies. However, calculating these integrals analytically without splitting them into sectors corresponding to individual diagrams poses a formidable mathematical challenge. We summarize the history and state of the art of this problem, including some natural connections to the theory of Bernoulli numbers and polynomials and multiple zeta values. We thank Andrei Davydychev and Tord Riemann for sharing with us their expertise on scalar off-shell N-point functions. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications New Techniques for Worldline Integration Article published earlier |
| spellingShingle | New Techniques for Worldline Integration Edwards, James P. Mata, C. Moctezuma Müller, Uwe Schubert, Christian |
| title | New Techniques for Worldline Integration |
| title_full | New Techniques for Worldline Integration |
| title_fullStr | New Techniques for Worldline Integration |
| title_full_unstemmed | New Techniques for Worldline Integration |
| title_short | New Techniques for Worldline Integration |
| title_sort | new techniques for worldline integration |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211358 |
| work_keys_str_mv | AT edwardsjamesp newtechniquesforworldlineintegration AT matacmoctezuma newtechniquesforworldlineintegration AT mulleruwe newtechniquesforworldlineintegration AT schubertchristian newtechniquesforworldlineintegration |