Feynman graphs in perturbative quantum field theory

TL;DR

This paper explores the mathematical structures underlying Feynman graphs in perturbative quantum field theory, focusing on their relations to periods, shuffle algebras, and multiple polylogarithms, and how these structures facilitate computational algorithms.

Contribution

It introduces new insights into the mathematical frameworks of Feynman graphs, connecting them to advanced algebraic and analytical concepts for improved calculations.

Findings

Feynman integrals relate to periods and polylogarithms

Algorithms derived from algebraic structures improve computation

Mathematical structures offer new perspectives in quantum field theory

Abstract

In this talk we discuss mathematical structures associated to Feynman graphs. Feynman graphs are the backbone of calculations in perturbative quantum field theory. The mathematical structures -- apart from being of interest in their own right -- allow to derive algorithms for the computation of these graphs. Topics covered are the relations of Feynman integrals to periods, shuffle algebras and multiple polylogarithms.