Name: rolf_at_HIDDEN-E-MAIL Date: 02/20/01-07:23:44 PM Z
Hi,
It is just a short-hand notation.
I.e.,
Eps[LorentzIndex[mu],
LorentzIndex[ComplexIndex[mu]],Momentum[k1],
Momentum[k2]]
is just
Eps[LorentzIndex[mu],
LorentzIndex[ComplexIndex[mu]],
LorentzIndex[dummy1], LorentzIndex[dummy2]] *
Pair[Momentum[k1],
LorentzIndex[dummy1]] * Pair[Momentum[k2],
LorentzIndex[dummy2]]
See also the examples in:
http://www.feyncalc.org/Contract/
Rolf
Quoting Timur Rashba <[rashba_at_HIDDEN-E-MAIL]>:
> Hello All!
>
> Could you explain this strange result:
>
> I was trying to calculate the trace
>
>
Tr[(m+DiracSlash[k1]).DiracMatrix[6].DiracMatrix[ComplexIndex[mu]].
>
(m+DiracSlash[k2]).DiracMatrix[mu].DiracMatrix[7]]
>
> and I’ve obtained
>
> 2 (\[ImaginaryI] Eps[LorentzIndex[mu],
LorentzIndex[ComplexIndex[mu]],
> Momentum[k1], Momentum[k2]] +
> Pair[LorentzIndex[mu], Momentum[k2]]
Pair[
> LorentzIndex[ComplexIndex[mu]],
Momentum[k1]] +
> Pair[LorentzIndex[mu], Momentum[k1]]
Pair[
> LorentzIndex[ComplexIndex[mu]],
Momentum[k2]] -
> Pair[LorentzIndex[mu],
LorentzIndex[ComplexIndex[mu]]] Pair[
> Momentum[k1], Momentum[k2]])
>
> What does the first term mean?
> Eps[LorentzIndex[mu],
LorentzIndex[ComplexIndex[mu]],Momentum[k1],
> Momentum[k2]])
> Why momenta k1 and k2 appeared in the indexes of LeviCivita?
> It’s not correct.
>
> Thank you in advance for the help.
>
> Timur
>
>
>
- - -
Rolf Mertig
Mertig Consulting
http://www.mertig.com