Tools and Tables for Quantum Field Theory Calculations


FeynCalc is a Mathematica package for symbolic evaluation of Feynman diagrams and algebraic calculations in quantum field theory and elementary particle physics.

Some features of FeynCalc are:

  • Passarino-Veltman reduction of one-loop amplitudes to standard scalar integrals
  • Tools for frequently occuring tasks like Lorentz index contraction, color factor calculation, Dirac matrix manipulation and traces, etc.
  • Tensor and Dirac algebra manipulations (including traces) in 4 or D dimensions
  • Generation of Feynman rules from a lagrangian
  • Tools for non-commutative algebra
  • SU(N) algebra
  • Tables of integrals, convolutions and Feynman rules
  • Special convolution, Mellin transform and other integral tables
  • Tools for calculating 2-loop propagator-type diagrams
  • FORM and FORTRAN code generation
  • Translation to and from FORM


For installation instructions please follow the steps outlined in our wiki. The impatient can simply type

Import["https://raw.githubusercontent.com/FeynCalc/feyncalc/master/install.m"]; InstallFeynCalc[]
in a Mathematica session.

The code may also be viewed and downloaded from our GitHub repository.

FeynCalc is covered by the GNU General Public License 3.

Copyright © 1990-2016 Rolf Mertig, Copyright © 1997-2016 Frederik Orellana, Copyright © 2014-2016 Vladyslav Shtabovenko

FeynCalc is free software: you can redistribute it and/or modify it under the terms of the GNU General Public License as published by the Free Software Foundation, either version 3 of the License, or (at your option) any later version.

FeynCalc is distributed in the hope that it will be useful, but WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more details.

You should have received a copy of the GNU General Public License along with FeynCalc. If not, see here.


FeynCalc is maintained and developed on a voluntarily basis by Rolf Mertig, Frederik Orellana and Vladyslav Shtabovenko.

We strive to keep all implemented functions documented in the reference guide.

Questions can be posted in the forum. New releases etc. are announced on the news page.

To support FeynCalc, please acknowledge our work when you use FeynCalc in your research. You can do so by citing the two FeynCalc papers: