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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.

J. M.'s missing motivation
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E. Chan-López
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    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 – bmf Feb 06 '23 at 00:47
  • Thanks, mate! Add your response and I'll gladly accept it. – E. Chan-López Feb 06 '23 at 00:53
  • Since, it's not much of a response other than saying that $\Gamma$-matrices are implemented as such, I am going to wait a bit to check if others have more elaborate answers. Nice catch by the way. I wrote something small on the undocumented functions thread a while ago and completely forgot about this command – bmf Feb 06 '23 at 00:55
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    You're right, we must wait for a more elaborate answer. That function seems interesting to me, since it's more specialized. – E. Chan-López Feb 06 '23 at 00:59
  • Hey mate, I hope you're okay. I haven't seen any activity from you in the community lately. – E. Chan-López Apr 12 '23 at 17:55
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    All is well, how are you? Just a lot of things to do, so I mainly do some maintenance here :-) – bmf Apr 17 '23 at 02:47
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    All good, just pulling out a bunch of backlogs. Glad to know you're okay, mate :-) – E. Chan-López Apr 17 '23 at 17:38

1 Answers1

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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

bmf
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