Status of Intersection Theory and Feynman Integrals

Abstract

We give a pedagogical review of the recently-introduced notion of a "scalar product" between Feynman integrals and how it helps us understand the analytic structure of the perturbative S-matrix. (This article is a contribution to the proceedings of the workshop "MathemAmplitudes 2019: Intersection Theory and Feynman Integrals" held in Padova, Italy on 18-20 December 2019.)

31 pages

References in corpus (4)

• Lectures on differential equations for Feynman integrals
• Resolution of singularities for multi-loop integrals
• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• On the computation of intersection numbers for twisted cocycles

Cited by in corpus (12)

• Decomposition of Feynman Integrals by Multivariate Intersection Numbers
• The SAGEX Review on Scattering Amplitudes, Chapter 3: Mathematical structures in Feynman integrals
• Crossing Symmetry in the Planar Limit
• Algorithms for minimal Picard-Fuchs operators of Feynman integrals
• Locally finite two-loop amplitudes for off-shell multi-photon production in electron-positron annihilation
• Chaos in a many-string scattering amplitude
• Algebraic branch points at all loop orders from positive kinematics and wall crossing
• Correlation functions on the lattice and twisted cocycles
• Non-perturbative computation of lattice correlation functions by differential equations
• Gauge and Gravity Amplitudes on the Celestial Sphere
• Geometric Recursion from Polytope Triangulations and Twisted Homology
• Co-homology of Differential Forms and Feynman diagrams