As Rolf correctly noticed, FeynCalc already offers routines for doing
tensor decompositions, so that there is actually no need to do it by hand.
Coming back to your particular example, there are two reasons why the
replacement doesn't work
1) The results returned by the FeynCalc functions are in the FeynCalc
internal representation, while your replacement rules uses the FeynCalc
external representation. To switch between the two use FCE and FCI
http://www.feyncalc.org/FeynCalcBook/FCE/
http://www.feyncalc.org/FeynCalcBook/FCI/
2) FeynCalc uses Dot operator to handle non-commutative objects like
Dirac or color matrices. So
GSD[k].GSD[l] actually means Dot[GSD[k],GSD[l]]
So the correct replacement rule is
s5 = FCE[ss4] /. {Dot[a___, GSD[l], b___] SPD[l, q] ->
Dot[a, GSD[q], b] SPD[l, l]/D}
But again, I would rather recommend using FeynCalc routines for this
kind of things
Cheers,
Vladyslav
Am 02.07.2014 21:39, schrieb Purnendu:
> Suppose I have do something like this :
>
> nprop = (MTD[\[Rho], \[Sigma]] -
> FVD[l, \[Rho]] FVD[l, \[Sigma]]/SPD[l, l])
>
> ss4 = Calc[GAD[\[Rho]].GSD[k].GSD[q].GAD[\[Sigma]].nprop] //
> DiracSimplify
>
> In this next step, I want to apply :
>
> s5 = ss4 /. {SPD[l, q] GSD[l] -> GSD[q] SPD[l, l]/D}
>
> How do I make this substitution to work?
>
> -Purnendu
>
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