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An Introduction to Motivic Feynman Integrals (2009.00426v2)
Published 31 Aug 2020 in math-ph, hep-th, math.AG, and math.MP
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 $\phi4$ quantum field theory is analysed in detail.
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