Alternatively, one could also use FIRE via FeynHelpers:
$LoadAddOns = {"FeynHelpers"};
<< FeynCalc`
tst1 = FAD[{l, mf}, {l, mf}, {l, mf}] (4 mf FVD[l, mu] FVD[l, nu] +
mf^3 MTD[mu, nu] - mf MTD[mu, nu] SPD[l, l]);
tst2 = TID[tst1, l]
FIREBurn[tst2, {l}, {}]
which also gives 0.
Cheers,
Vladyslav
> Yes, there you need to use TARCER.
> The following returns 0:
>
> $LoadTARCER = True; $LoadFeynArts = $LoadPhi = False;
> $FeynCalcStartupMessages = False;
> Needs["HighEnergyPhysics`FeynCalc`"];
> tst1 = FeynAmpDenominator[PropagatorDenominator[Momentum[l, D],
> Sqrt[mf^2]], PropagatorDenominator[Momentum[l, D], Sqrt[mf^2]],
> PropagatorDenominator[Momentum[l, D], Sqrt[mf^2]]]*
> (mf^3*Pair[LorentzIndex[mu, D], LorentzIndex[nu, D]] +
> 4*mf*Pair[LorentzIndex[mu, D], Momentum[l, D]]*
> Pair[LorentzIndex[nu, D], Momentum[l, D]] -
> mf*Pair[LorentzIndex[mu, D], LorentzIndex[nu, D]]*
> Pair[Momentum[l, D], Momentum[l, D]]);
> TarcerRecurse[ToFI[OneLoopSimplify[tst1, l], {l}, {0}]]
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