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 ϕ4 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
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
This publication is cited in the following 2 articles:
Philip Candelas, Xenia de la Ossa, Pyry Kuusela, Joseph McGovern, “Flux vacua and modularity for Z2 symmetric Calabi-Yau manifolds”, SciPost Phys., 15:4 (2023)
Oliver Schnetz, Karen Yeats, “c2 Invariants of Hourglass Chains via Quadratic Denominator Reduction”, SIGMA, 17 (2021), 100, 26 pp.