An Introduction to Motivic Feynman Integrals
This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric and categorical structures underlying Feynman graphs is revi...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2021 |
| Main Author: | |
| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2021
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/211317 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | An Introduction to Motivic Feynman Integrals. Claudia Rella. SIGMA 17 (2021), 032, 56 pages |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862729545104228352 |
|---|---|
| author | Rella, Claudia |
| author_facet | Rella, Claudia |
| citation_txt | An Introduction to Motivic Feynman Integrals. Claudia Rella. SIGMA 17 (2021), 032, 56 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric and categorical structures underlying Feynman graphs is reviewed up to the current state of research. The example of primitive log-divergent Feynman graphs in scalar massless ⁴ quantum field theory is analysed in detail.
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| first_indexed | 2026-04-17T14:48:45Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-211317 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-04-17T14:48:45Z |
| publishDate | 2021 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Rella, Claudia 2025-12-29T11:09:52Z 2021 An Introduction to Motivic Feynman Integrals. Claudia Rella. SIGMA 17 (2021), 032, 56 pages 1815-0659 2020 Mathematics Subject Classification: 81-02;14-02;81Q30;81T18;81T15;14C15;14C30; 14F40;11R32 arXiv:2009.00426 https://nasplib.isofts.kiev.ua/handle/123456789/211317 https://doi.org/10.3842/SIGMA.2021.032 This article gives a short step-by-step introduction to the representation of parametric Feynman integrals in scalar perturbative quantum field theory as periods of motives. The application of motivic Galois theory to the algebro-geometric and categorical structures underlying Feynman graphs is reviewed up to the current state of research. The example of primitive log-divergent Feynman graphs in scalar massless ⁴ quantum field theory is analysed in detail. I thank Francis Brown and Lionel Mason for useful discussions. I thank the three anonymous referees for their detailed reports that have provided a valuable guide in improving the paper. Finally, I thank Evgeny Mukhin and the rest of the organisers of the Conference on Representation Theory and Integrable Systems (ETH Zurich, 2019) for the opportunity to speak and to contribute to the special issue. This work is partially supported by the Italian Department of Education, Research and University (Torno Subito 13474/19.09.2018 POR-Lazio-FSE/20142020) and the Swiss National Centre of Competence in Research SwissMAP (NCCR 51NF40141869 The Mathematics of Physics). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications An Introduction to Motivic Feynman Integrals Article published earlier |
| spellingShingle | An Introduction to Motivic Feynman Integrals Rella, Claudia |
| title | An Introduction to Motivic Feynman Integrals |
| title_full | An Introduction to Motivic Feynman Integrals |
| title_fullStr | An Introduction to Motivic Feynman Integrals |
| title_full_unstemmed | An Introduction to Motivic Feynman Integrals |
| title_short | An Introduction to Motivic Feynman Integrals |
| title_sort | introduction to motivic feynman integrals |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/211317 |
| work_keys_str_mv | AT rellaclaudia anintroductiontomotivicfeynmanintegrals AT rellaclaudia introductiontomotivicfeynmanintegrals |