FeynCalc goes multiloop

TL;DR

This paper introduces new multiloop calculation functionalities in the open-source FeynCalc package, including topology identification, master integral search, and Feynman parametric derivation, enhancing its capabilities for complex quantum field theory computations.

Contribution

It adds novel multiloop analysis tools to FeynCalc, such as topology algorithms and integral representations, advancing automated multiloop Feynman integral calculations.

Findings

Implemented topology identification with Pak algorithm

Enabled automatic derivation of Feynman parametric representations

Package functionalities are ready for official release

Abstract

We report on the new functionality of the open-source Mathematica package FeynCalc relevant for multiloop calculations. In particular, we focus on such tasks as topology identification by means of the Pak algorithm, search for equivalent master integrals and their graph representations as well as automatic derivations of Feynman parametric representations for a wide class of multiloop integrals. The functions described in this report are expected to be finalized with the official release of FeynCalc 10. The current development snapshot of the package including the documentation is publicly available on the project homepage. User feedback is highly encouraged.