I am calculating products like

enter image description here

in mathematica. In the given relations eta's are four vectors, $\gamma$'s are the Dirac matrices, $\sigma^{\mu\nu}$ is the anticommutation of the gamma matrices and some constants are involved.

I have written a mathematica code component be component which is correct and the results are fine.

But the component wise code is too long and cumbersome.

How to write a compact code for such type of products.

Also I do not know how to write the code for

$\eta_\mu \eta_\nu (p^\mu k^\nu - k^\mu p^\nu)$ where p and k are four vectors. Any help will be appreciated. Thank you. Some one might help me in tagging the correct groups.

  • $\begingroup$ The GammaMaP package might be relevant for your problem: arxiv.org/abs/1905.00429 $\endgroup$ Jan 19 at 14:53
  • $\begingroup$ Welcome to MMA Stackexchange. Perhaps if you share your code, then people might be able to help you more. $\endgroup$
    – Dunlop
    Jan 19 at 18:19

1 Answer 1


I have successfully implemented the products like in the given structure.

`h_T50t = gT Sum[
Signature[{a, b, c, d}] ConjugateTranspose[
  etmu0l[[a]]] ConjugateTranspose[
  etmutl[[b]]] (pBmul[[c]] kDmul[[d]] ), {a, 1, 4}, {b, 1, 4}, {c,
  1, 4}, {d, 1, 4}] * (2 fT)/(mB + mD) // FullSimplify`    

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