Computer algebra tools for Feynman integrals and related multi-sums

TL;DR

This paper discusses computer algebra tools and software packages developed over ten years to evaluate and simplify Feynman integrals and related multi-sums in perturbative quantum field theory calculations.

Contribution

It introduces specialized computer algebra tools and packages designed for simplifying Feynman integrals and solving systems of differential equations in QCD calculations.

Findings

Development of algorithms for nested sums and integrals

Implementation of packages for Feynman integral evaluation

Application to perturbative QCD calculations

Abstract

In perturbative calculations, e.g., in the setting of Quantum Chromodynamics (QCD) one aims at the evaluation of Feynman integrals. Here one is often faced with the problem to simplify multiple nested integrals or sums to expressions in terms of indefinite nested integrals or sums. Furthermore, one seeks for solutions of coupled systems of linear differential equations, that can be represented in terms of indefinite nested sums (or integrals). In this article we elaborate the main tools and the corresponding packages, that we have developed and intensively used within the last 10 years in the course of our QCD-calculations.