An Introduction to Motivic Feynman Integrals

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 ${\varphi }^4$ quantum field theory is analysed in detail.

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Cited by in corpus (4)

• Position Space Equations for Banana Feynman Diagrams
• Flux Vacua and Modularity for ${\mathbb{Z}}_2$ Symmetric Calabi-Yau Manifolds
• Algebraic Interplay between Renormalization and Monodromy
• $c_2$ invariants of hourglass chains via quadratic denominator reduction