Name: Vladyslav Shtabovenko (email_not_shown)
Date: 06/29/15-11:51:41 AM Z

Hi,

frankly speaking, I don't quite see what is the issue
with FeynCalc's result. The integral you write is clearly
scaleless, such that in Dimensional Regularization (which is always
assumed in FeynCalc) you can make a shift k->k+q1 and obtain

k^mu / (k-q1)^2 = (k^mu + q1^mu) / k^2 = k^mu /k^2 + q1^mu /k^2

Now the first integral vanishes b/c it is antisymmetric under k-> -k.
The second integral is scaleless and is set to zero in dim.reg,
following the general rule that

\int d^D k (k^2)^a = 0 for any a.

This is how 0 comes out.

I'm not sure that I understand how you arrive to q1^mu / (k-q1)^2

Even if you don't set scaleless integrals to zero, the formal result of
the tensor decomposition is given by

int = FCI[Tdec[{{k, mu}}, {q1}, List -> False] FAD[k - q1]]

or

(int /. k -> k + q1) // MomentumExpand // ExpandScalarProduct

which is of course still scaleless and hence zero in dim. reg.

Cheers,

Am 29.06.2015 um 00:24 schrieb SUN Qingfeng:
> Input:
> test = FVD[k, \[Mu]] FAD[k - q1] // FCI
> TID[test, k]
>
> Output:
> 0
>
> But I think the answer should be:?
> FVD[q1, \[Mu]] FAD[k - q1]
>
> Which answer should be correct?
>
> My version Info:
> Mathematica 8.0 FeynCalc 9.0
>

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