FeynCalc 10: Do multiloop integrals dream of computer codes?

TL;DR

FeynCalc 10 introduces advanced multiloop calculation capabilities, improved tensor reduction, and enhanced tools for quantum field theory computations within Mathematica, significantly aiding particle physics research.

Contribution

This version of FeynCalc provides novel features for multiloop integrals, tensor reduction, and differential equations, advancing computational tools in quantum field theory.

Findings

Enhanced multiloop calculation features

Improved tensor reduction and scalar product rewriting

Support for differential equations and iterated integrals

Abstract

In this work we report on a new version of FeynCalc, a Mathematica package widely used in the particle physics community for manipulating quantum field theoretical expressions and calculating Feynman diagrams. Highlights of the new version include greatly improved capabilities for doing multiloop calculations, including topology identification and minimization, optimized tensor reduction, rewriting of scalar products in terms of inverse denominators, detection of equivalent or scaleless loop integrals, derivation of Symanzik polynomials, Feynman parametric as well as graph representation for master integrals and initial support for handling differential equations and iterated integrals. In addition to that, the new release also features completely rewritten routines for color algebra simplifications, inclusion of symmetry relations between arguments of Passarino--Veltman functions, tools for determining matching coefficients and quantifying the agreement between numerical results, improved export to LaTeX and first steps towards a better support of calculations involving light-cone vectors.