Periods and Feynman amplitudes

Abstract

Feynman amplitudes in perturbation theory form the basis for most predictions in particle collider experiments. The mathematical quantities which occur as amplitudes include values of the Riemann zeta function and relate to fundamental objects in number theory and algebraic geometry. This talk reviews some of the recent developments in this field, and explains how new ideas from algebraic geometry have led to much progress in our understanding of amplitudes. In particular, the idea that certain transcendental numbers, such as $\pi$, can be viewed as a representation of a group, provides a powerful framework to study amplitudes which reveals many hidden structures.

Talk given at the ICMP, Santiago de Chile, July 2015

References in corpus (9)

• Algorithms for the symbolic integration of hyperlogarithms with applications to Feynman integrals
• Lectures on differential equations for Feynman integrals
• The two-loop sunrise graph in two space-time dimensions with arbitrary masses in terms of elliptic dilogarithms
• A Symbol of Uniqueness: The Cluster Bootstrap for the 3-Loop MHV Heptagon
• Feynman integrals and hyperlogarithms
• Feynman Amplitudes and Cosmic Galois group
• Framings for graph hypersurfaces
• Galois theory, motives and transcendental numbers
• Ambiguity theory, old and new

Cited by in corpus (5)

• Matroid connectivity and singularities of configuration hypersurfaces
• Relativistic causality and position space renormalization
• Periods and Applications
• On p-adic Frobenius lifts and p-adic periods, from a Deformation Theory viewpoint
• On periods: from global to local