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Symmetry, Integrability and Geometry: Methods and Applications, 2021, Volume 17, 032, 56 pp.
DOI: https://doi.org/10.3842/SIGMA.2021.032 (Mi sigma1715) 		 
This article is cited in 2 scientific papers (total in 2 papers)

An Introduction to Motivic Feynman Integrals

Claudia Rella

Section de Mathématiques, Université de Genève, Genève, CH-1211 Switzerland
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DOI: https://doi.org/10.3842/SIGMA.2021.032
Abstract: 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 $\phi^4$ quantum field theory is analysed in detail.
Keywords: scattering amplitudes, Feynman diagrams, multiple zeta values, Hodge structures, periods of motives, Galois theory, Tannakian categories.
Funding agency Grant number
Italian Department of Education, Research and University 13474/19.09.2018 POR-Lazio-FSE/2014-2020
Swiss National Science Foundation NCCR 51NF40-141869
This work is partially supported by the Italian Department of Education, Research and University (Torno Subito 13474/19.09.2018 POR-Lazio-FSE/2014-2020) and the Swiss National Centre of Competence in Research SwissMAP (NCCR 51NF40-141869 The Mathematics of Physics).
Received: August 30, 2020; in final form March 3, 2021; Published online March 26, 2021
Bibliographic databases:
Document Type: Article
MSC: 81-02, 14-02, 81Q30, 81T18, 81T15, 14C15, 14C30, 14F40, 11R32
Language: English
Citation: Claudia Rella, “An Introduction to Motivic Feynman Integrals”, SIGMA, 17 (2021), 032, 56 pp.
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Symmetry, Integrability and Geometry: Methods and Applications
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