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Searching for information on undocumented functions here, I found that there are no references about the use of the undocumented function Internal`DiracGammaMatrix.

Does anyone in the community have any information on this?

I appreciate any help in advance.

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    $\begingroup$ The only thing I know is that there are 3 different bases; Majorana, chiral, and Dirac. For instance try MatrixForm /@Table[Internal`DiracGammaMatrix[k, "Basis" -> "Chiral"], {k, 4}]. Likewise for the other two choices $\endgroup$
    – bmf
    Feb 6, 2023 at 0:47
  • $\begingroup$ Thanks, mate! Add your response and I'll gladly accept it. $\endgroup$ Feb 6, 2023 at 0:53
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    $\begingroup$ You're right, we must wait for a more elaborate answer. That function seems interesting to me, since it's more specialized. $\endgroup$ Feb 6, 2023 at 0:59
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    $\begingroup$ All is well, how are you? Just a lot of things to do, so I mainly do some maintenance here :-) $\endgroup$
    – bmf
    Apr 17, 2023 at 2:47
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    $\begingroup$ All good, just pulling out a bunch of backlogs. Glad to know you're okay, mate :-) $\endgroup$ Apr 17, 2023 at 17:38

1 Answer 1

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The $\Gamma$-matrices are built-in, albeit undocumented. This is the Internal`DiracGammaMatrix command.

The are 3 choices for the basis of the matrices, namely chiral, Dirac and Majorana. From the above choices, the chiral basis is the default.

Table[Internal`DiracGammaMatrix[k, "Basis" -> "Chiral"] // 
  MatrixForm, {k, 4}]
Table[Internal`DiracGammaMatrix[k] // MatrixForm, {k, 4}]

ch

Table[Internal`DiracGammaMatrix[k, "Basis" -> "Dirac"] // 
  MatrixForm, {k, 4}]

dirac

Table[Internal`DiracGammaMatrix[k, "Basis" -> "Majorana"] // 
  MatrixForm, {k, 4}]

majo

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