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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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2021
Автор: Rella, Claudia
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2021
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211317
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати: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
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author Rella, Claudia
author_facet Rella, Claudia
citation_txt An Introduction to Motivic Feynman Integrals. Claudia Rella. SIGMA 17 (2021), 032, 56 pages
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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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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
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