Name: Ula Date: 05/19/17-01:11:12 PM Z
Dear Vladyslav,
I was using
AmpSquare := Tr[…]
(rather than =), so in your case ID is unknown to FeynCalc at the time of evaluation.
I also guess that the Dependence of Res2 on GA[] was somehow caused by DeclareNonCommutative – in my original example Res2 was a ``number”, as it should be, even though it was a wrong number.
Thanks and best wishes,
Ula
> Dear Ula,
>
> I apologize, I’m afraid I skimmed through your code only
> very briefly and overlooked that you already define L and
> R as GA[6] and GA[7], instead of first using the
sole symbols in the
> calculation.
>
> On the other hand, now I’m afraid that I’m not able to reproduce
your
> wrong result. With FeynCalc 9.2 this (now without
DeclareNonCommutative)
>
> R = GA[6];
> L = GA[7];
> yiPR = YiPR L + YiPRCC R;
> ys1 = Ys1 L + Ys1CC R;
> ys2 = Ys2 L + Ys2CC R;
> SetMandelstam[s, t, u, p1, p2, -q1, -q2, mc1, mc2, ms1,
ms2];
>
> AmpSquare =
> Tr[yiPR.(GS[p1] - mc1 ID).ys1.(GS[p2 - q2] + mb
ID).ys2.(GS[p2] +
> mc2 ID)] // Simplify;
>
> ID = 1; Res1 = AmpSquare
>
> Clear[ID, Res2]
> ID = GA[6] + GA[7];
> Res2 = AmpSquare
>
> (Res1 - Res2) // Simplify
> % // DiracSimplify[#, DiracSubstitute67 -> True] &
>
> yields 0 as it should (c.f. the attached notebook)
>
>
> As to your second comment, in FeynCalc there are no explicit
Dirac
> indices, and hence no special unit matrix in the Dirac space.
> This means, that when you compute a Dirac trace, all the Dirac
> matrices should be spelled out explicitly.
>
>
> Otherwise you get such strange results with Dirac matrices
remaining
> after the trace. Here the issue is really that FeynCalc does not
know
> what is ID and assumes it to be a c-number, i.e. something free
of
> Dirac matrices.
>
> Again, you could do
>
> R = GA[6];
> L = GA[7];
> yiPR = YiPR L + YiPRCC R;
> ys1 = Ys1 L + Ys1CC R;
> ys2 = Ys2 L + Ys2CC R;
>
> SetMandelstam[s, t, u, p1, p2, -q1, -q2, mc1, mc2, ms1,
ms2];
> DeclareNonCommutative[ID];
>
> AmpSquare =
> DiracTrace[
> yiPR.(GS[p1] - mc1 ID).ys1.(GS[p2 - q2] + mb
ID).ys2.(GS[p2] +
> mc2 ID), DiracTraceEvaluate -> True]
>
> However, in this case DiracTrace will abort evaluation, once it
> encounters a trace over ID that it does not know how to handle.
>
> Cheers,
> Vladyslav
>
> Am 19.05.2017 um 12:15 schrieb Ula:
>> Dear Vladyslav,
>>
>> I don’t have much experience with FeynCalc (I hope this will
change soon), maybe that is why I don’t understand why should I use
DeclareNonCommutative[L, R]. I mean, L and R are just
abbreviations for internal FeynCalc objects (I was using SetDelayed in
my definitions of AmpSquare).
>>
>> I checked that with your tip it works correctly, but, to be
honest, the fact that Res2 still depends on chiral projectors is even
more strange.
>>
>> Best regards,
>> Ula
>>
>>> Dear Ula,
>>>
>>> in this case you are missing a declaration of L and R
>>> as noncommutative quantities.
>>>
>>> By default, FeynCalc will treat every symbol that has not
been
>>> explicitly declared to be noncommutatuve, as a c-number. The
following
>>> works fine
>>>
>>> DeclareNonCommutative[L, R]
>>> R = GA[6];
>>> L = GA[7];
>>> yiPR = YiPR L + YiPRCC R;
>>> ys1 = Ys1 L + Ys1CC R;
>>> ys2 = Ys2 L + Ys2CC R;
>>> SetMandelstam[s, t, u, p1, p2, -q1, -q2, mc1, mc2, ms1,
ms2];
>>>
>>> AmpSquare =
>>> Tr[yiPR.(GS[p1] - mc1 ID).ys1.(GS[p2 - q2] +
mb ID).ys2.(GS[p2] +
>>> mc2 ID)] // Simplify;
>>>
>>> ID = 1; Res1 = AmpSquare
>>>
>>> Clear[ID, Res2]
>>> ID = GA[6] + GA[7];
>>> Res2 = AmpSquare
>>>
>>> (Res1 - Res2) // DiracSimplify[#, DiracSubstitute67 ->
True] &
>>>
>>> Here DiracSubstitute67 merely replaces GA[6] and
GA[7] by their
>>> explicit values, i.e. 1/2(1+GA[5]) and
1/2(1-GA[5]) respectively.
>>> Otherwise the difference is proportional to
(GA[6]+GA[7]-1)
>>>
>>> Cheers,
>>> Vladyslav
>>>
>>>
>>> Am 19.05.2017 um 11:24 schrieb Ula:
>>>> Dear Vladyslav,
>>>>
>>>> Thanks for the fast reply and your great work with FeynCalc. I
checked that many examples with chiral projectors indeed yield correct
results now, but not all of them. In the example below, Res1 is
consistent with my own calculations.
>>>>
>>>> (*Definitions*)
>>>>
>>>> In[2]:= R = GA[6];
>>>>
>>>> In[3]:= L = GA[7];
>>>>
>>>> In[4]:= yiPR = YiPR L + YiPRCC R;
>>>>
>>>> In[5]:= ys1 = Ys1 L + Ys1CC R;
>>>>
>>>> In[6]:= ys2 = Ys2 L + Ys2CC R;
>>>>
>>>> In[7]:= SetMandelstam[s, t, u, p1, p2, -q1, -q2,
mc1, mc2, ms1, ms2];
>>>>
>>>> In[8]:= AmpSquare :=
*>>>> Tr[yiPR.(GS[p1] - mc1 ID).ys1.(GS[p2 - q2]