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This is related to the Mathematica package FeynCalc.

Is there a way to simplify the metric? I mean in the sense that when I evaluate something and I get a long expression involving lots of $$g^{12}$$ and other off diagonal entries, is there a way to let Mathematica know that I work in a flat space so that these off diagonal entries should be set to zero?

An example:

Tr[GA[1].GA[2].DiracSlash[k].DiracSlash[p]]

gives

$$\mathrm{Tr}[\gamma^1\gamma^2\not{k}\not{p}] = 4(g^{12}k\cdot p+k^2p^1-k^1p^2)$$

where the indices might or might not be indices or powers. I don't know how to interpret that. I can only reside to dimension counting to guess which is which in larger expressions.

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  • $\begingroup$ FeynCalc is actually not intended for working with explicit components of metric tensors and 4-vectors (unless you very well understand what you are doing), so whenever you get a result that contains such explicit components I would expect that there was a mistake in the input. It would be therefore very helpful if you could post the smallest working example of your code that leads to this kind of result. $\endgroup$
    – vsht
    Oct 12, 2015 at 13:28
  • $\begingroup$ @vsht OK I'll update the question. $\endgroup$ Oct 12, 2015 at 13:43
  • $\begingroup$ So with GA[1] and GA[2] you really mean particular Dirac matrices $$\gamma^1$$ and $$\gamma^2$$ right? $\endgroup$
    – vsht
    Oct 12, 2015 at 13:58
  • $\begingroup$ Yes that is correct. $\endgroup$ Oct 12, 2015 at 13:59

1 Answer 1

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In principle, you can set the explicit values of the metric tensor by hand, e.g.

Inner[Set, Table[FCI@MT[i, j], {i, 0, 3}, {j, 0, 3}], {{1, 0, 0,0}, {0, -1, 0, 0}, {0, 0, -1, 0}, {0, 0, 0, -1}}];

Then

Tr[GA[1].GA[2].DiracSlash[k].DiracSlash[p]]

returns only

$$ 4 (k^2 p^1 - k^1 p^2) $$

But since this is not the usual way FeynCalc is meant to be used, do not be surprised that for explicit indices many simplifications are simply not implemented.

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  • $\begingroup$ Thanks for your answer. I think I wont touch anything. It's perhaps best if I rewrite my expressions in a more general form and simplify as much as I can by hand before plugging into FeynCalc. $\endgroup$ Oct 12, 2015 at 14:24

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