Multi-valued Feynman Graphs and Scattering Theory

Abstract

We outline ideas to connect the analytic structure of Feynman amplitudes to the structure of Karen Vogtmann's {\em Outer Space}. We focus on the role of cubical chain complexes in this context, and also investigate the bordification problem in the example of the 3-edge banana graph.

31 pages, figures use colors, minor changes, as to appear in the Proceedings of the conference {\em Elliptic Integrals, Elliptic Functions and Modular Forms in Quantum Field Theory}, DESY-Zeuthen, October 2017, Johannes Blümlein et.al., eds

References in corpus (5)

• The massless higher-loop two-point function
• Feynman amplitudes and Landau singularities for 1-loop graphs
• Feynman amplitudes on moduli spaces of graphs
• On the bordification of outer space
• The sunrise integral and elliptic polylogarithms

Cited by in corpus (3)

• Tropical Monte Carlo quadrature for Feynman integrals
• Momentum Space Landau Equations Via Isotopy Techniques
• Algebraic Interplay between Renormalization and Monodromy