Prefactors in scalar products

[mhutt21]

Hi, I am having a (perhaps quite basic) problem with expanding scalar products. Essentially I have a large expression which contains many scalar products SP[P,Q] and then I have a replacement rule for one of the momenta in each scalar product. The replacement rule is of the form P -> a Momentum[P1] + b Momentum[P2] where a and b are constants (they are actually ratios of other scalar products). Is there a way that I can tell FeynCalc that a and b are not part of the momenta, so they can be taken out of the scalar product?

i.e. the following
product = SP[P,Q]
Pnew = a Momentum[P1] + b Momentum[P2]
product /. {P -> Pnew} // ExpandScalarProduct
yields Q . (a P1) + Q . (b P2) but I need it to give a (Q . P1) + b (Q . P2) since a and b are just constants. Is there a way to do this?

Thanks in advance!

[vsht]

Hi,

for that you need to use FCVariable

https://feyncalc.github.io/FeynCalcBookDev/FCVariable.html

DataType[a, FCVariable] = True;
DataType[b, FCVariable] = True;

ExpandScalarProduct[SP[P,Q]/.P->a P1 +b P2]
StandardForm[%]
(*a Pair[Momentum[P1], Momentum[Q]] + b Pair[Momentum[P2], Momentum[Q]]*)

Cheers,
Vladyslav