An Introduction to Motivic Feynman Integrals

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dc.contributor.authorRella, Claudia
dc.date.accessioned2025-12-29T11:09:52Z
dc.date.issued2021
dc.description.abstractThis 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 𝜙⁴ quantum field theory is analysed in detail.
dc.description.sponsorshipI 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).
dc.identifier.citationAn Introduction to Motivic Feynman Integrals. Claudia Rella. SIGMA 17 (2021), 032, 56 pages
dc.identifier.doihttps://doi.org/10.3842/SIGMA.2021.032
dc.identifier.issn1815-0659
dc.identifier.other2020 Mathematics Subject Classification: 81-02;14-02;81Q30;81T18;81T15;14C15;14C30; 14F40;11R32
dc.identifier.otherarXiv:2009.00426
dc.identifier.urihttps://nasplib.isofts.kiev.ua/handle/123456789/211317
dc.language.isoen
dc.publisherІнститут математики НАН України
dc.relation.ispartofSymmetry, Integrability and Geometry: Methods and Applications
dc.statuspublished earlier
dc.titleAn Introduction to Motivic Feynman Integrals
dc.typeArticle

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Symmetry, Integrability and Geometry: Methods and Applications, 2021, том 17, випуск за цей рік