New Developments in FeynCalc 9.0

TL;DR

FeynCalc 9.0 enhances a semi-automatic Mathematica toolkit for symbolic quantum field theory by advancing 1) tensor decomposition to arbitrary rank, 2) a fully integrated partial fractioning algorithm, 3) seamless IBP-reduction interfacing, 4) advanced extraction and management of loop integrals, 5) a robust interface with FeynArts, 6) finer control over expansions, and 7) explicit SU(N) fundamentals via SUNTF. Together with improved NRQCD support and clear guidance for non-relativistic EFTs, these features enable more efficient and flexible multi-loop and effective-theory calculations while preserving the user-directed workflow that distinguishes FeynCalc from fully automatic tools. The work emphasizes interoperability with external IBP packages, robust diagrammatic input, and practical demonstrations, reinforcing FeynCalc’s relevance for specialized, non-trivial perturbative calculations. Overall, the update broadens applicability to NRQCD matching, multi-loop analyses, and non-covariant EFT contexts, while maintaining openness to future integrations and extensions within the high-energy physics software ecosystem.

Abstract

In this note we report on the new version of FeynCalc, a Mathematica package for symbolic semi-automatic evaluation of Feynman diagrams and algebraic expressions in quantum field theory. The main features of version 9.0 are: improved tensor reduction and partial fractioning of loop integrals, new functions for using FeynCalc together with tools for reduction of scalar loop integrals using integration-by-parts (IBP) identities, better interface to FeynArts and support for SU(N) generators with explicit fundamental indices.