I want to calculate traces of Dirac matrices with a program like Mathematica. I found the package FeynCalc or Tracer.m but they seem to be outdated.

Are there any better / newer solutions to this? I am also open to other Software than Mathematica.

  • 1
    $\begingroup$ First of all, FeynCalc is actively developed. Second, Tracer, although not actively developed, is still very much used in the HEP community because it provides a stable implementation of the Dirac algebra in the Breitenlohner-Maison-t'Hooft-Veltman scheme. Third, FORM as suggested by Suzu Hirose is of course a good choice, but the learning curve is much steeper than that of Mathematica. Finally, GiNaC and sympy also can compute traces, if you are more comfortable with C++ or Python. But at the end, in terms of performance FORM is the fastest thing on the market. $\endgroup$
    – vsht
    Oct 21, 2016 at 9:42
  • $\begingroup$ I've removed a couple of comments which were more like answers, but which didn't meet the resource-recommendation guidelines mentioned in the question banner. $\endgroup$
    – rob
    Aug 6, 2017 at 3:42
  • $\begingroup$ @vsht have looked into HEPMath? How about Package-X $\endgroup$
    – QuantumDot
    Aug 8, 2017 at 12:29
  • $\begingroup$ AFAIK HEPMath is not actively developed anymore, since the author left academia. Package-X is closed source, so I cannot say much about the algorithms used. Still, it is definitely not faster on traces than FORM. $\endgroup$
    – vsht
    Nov 15, 2017 at 7:23

1 Answer 1


FORM is a well-known system for these calculations. There is a Wikipedia page about it.


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