Multi-loop techniques for massless Feynman diagram calculations

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.

Comments: Review article. LaTeX file with feynMF package. (v2) references added and minor typos corrected. 65 pages, 8 figures. (v1) 64 pages, 8 figures