Hi,
Cartesian stuff is officially available (and also documented) since
FeynCalc 9.3,
but it's true that there are virtually no examples on using it in real
calculations.
Some (partly outdated) details can be found in Sec 24.2 of
https://inspirehep.net/literature/1670088
There should be a publication addressing NR calculations with FeynCalc
appearing rather soon O(1-2 weeks).
Long story short, what you need are CLC and CLCD
https://feyncalc.github.io/FeynCalcBook/ref/CLC.html
https://feyncalc.github.io/FeynCalcBook/ref/CLCD.html
CLC[a, b, c] CLC[a, b, e] // Contract // FCE
(*2 KD[c, e]*)
CLCD[a, b, c] CLCD[a, b, e] // Contract // FCE
(*6 KDD[c, e] - 5 D KDD[c, e] + D^2 KDD[c, e]*)
Notice that here Cartesian tensors live in D-1 dimensions
because they are defined to be spatial pieces of the corresponding
Lorentz tensors. That is, you have need to consider D-1 -> 3, not D->3
to get the right limit.
Cheers,
Vladyslav
Am 24.06.20 um 13:18 schrieb Nathan:
> Hi there,
>
> I am trying to do some Levi-Civita contractions in D = 3 but it doesn't seem to work. For example, I can do
>
> LC[a,b,c,d]LC[a,b,c,e]//Contract
>
> in D=4 and get the contraction (the metric), but doing
>
> LC[a,b,c]LC[a,b,e]//Contract
>
> in D = 3 does not give me the equivalent. I have tried using SetOptions[LeviCivita, Dimension -> 3] and replacing LC with LCD, but ultimately it only seems to work with four index tensors.
>
> Any ideas how I can implement this for three-index LC's?
>
> Thanks.
>
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