The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals

Understand

Dimensionally-regulated Feynman integrals are a cornerstone of all perturbative computations in quantum field theory.

• They are known to exhibit a rich mathematical structure, which has led to the development of powerful new techniques for their computation.
• We review some of the most recent advances in our understanding of the analytic structure of multiloop Feynman integrals in dimensional regularisation.
• In particular, we give an overview of modern approaches to computing Feynman integrals using differential equations, and we discuss some of the properties of the functions that appear in the solutions.