Multi-loop techniques for massless Feynman diagram calculations

TL;DR

This paper reviews advanced multi-loop techniques for calculating massless Feynman diagrams in quantum field theory, highlighting methods like integration by parts, the method of uniqueness, and Gegenbauer polynomials, with historical context and examples up to five loops.

Contribution

It provides a comprehensive overview of multiple analytical techniques for multi-loop massless Feynman diagram calculations, including new examples up to five loops.

Findings

Summarizes key multi-loop calculation methods.

Provides concrete five-loop diagram examples.

Highlights historical development of techniques.

Abstract

We review several multi-loop techniques for analytical massless Feynman diagram calculations in relativistic quantum field theories: integration by parts, the method of uniqueness, functional equations and the Gegenbauer polynomial technique. A brief, historically oriented, overview of some of the results obtained over the decades for the massless 2-loop propagator-type diagram is given. Concrete examples of up to $5$-loop diagram calculations are also provided.