# Choosing Minkowski metric in Feyncalc

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.

• 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.
– vsht
Oct 12, 2015 at 13:28
• @vsht OK I'll update the question. Oct 12, 2015 at 13:43
• So with GA[1] and GA[2] you really mean particular Dirac matrices $$\gamma^1$$ and $$\gamma^2$$ right?
– vsht
Oct 12, 2015 at 13:58
• Yes that is correct. Oct 12, 2015 at 13:59

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.

• 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. Oct 12, 2015 at 14:24