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ComplexConjugate[DiracGamma[5]] // StandardForm

returns

-DiracGamma[5]

Instead of simply

DiracGamma[5]

DiracGamma[5] is Hermitian is it not? Am I missing something?

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  • $\begingroup$ In any case this is closely related Proof of the Dirac-γ matrices identity. $\endgroup$
    – Artes
    Commented Feb 1, 2018 at 18:57
  • $\begingroup$ Not quite! I am addressing a specific issue with feyncalc functions. $\endgroup$
    – Decebalus
    Commented Feb 1, 2018 at 22:09

1 Answer 1

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I think ComplexConjugate works on products of Dirac matrices assuming it is sandwiched between $u$ and/or $v$ spinors. Observe:

SpinorUBar[k1, m].GA[5].SpinorU[p1, m] // ComplexConjugate

Output:

enter image description here

Now the minus sign makes sense.

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  • $\begingroup$ Yeah I think I figured this out as well, because I get the correct expression at the end of the day when the gamma5 matrix is between two spinors. $\endgroup$
    – Decebalus
    Commented Feb 1, 2018 at 16:55

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