Transcendental numbers and the topology of three-loop bubbles

TL;DR

This paper proves that all transcendental numbers required for three-loop vacuum Feynman diagram calculations can be derived from simpler spectacle topology diagrams, simplifying the understanding of these complex integrals.

Contribution

It introduces a method to obtain all necessary transcendental numbers from simpler diagram topologies, advancing the computational approach in quantum field theory.

Findings

All transcendental numbers for three-loop diagrams are obtainable from spectacle topology.

Simplification of complex integrals through topology reduction.

Enhanced understanding of the mathematical structure of Feynman integrals.

Abstract

We present a proof that all transcendental numbers that are needed for the calculation of the master integrals for three-loop vacuum Feynman diagrams can be obtained by calculating diagrams with an even simpler topology, the topology of spectacles.