SPD[a, b]
denotes a D-dimensional scalar product.
SPD[a, b]
is transformed into ScalarProduct[a, b,Dimension->D]
by FeynCalcInternal
.
SPD[p]
is the same as SPD[p,p]
(=p^2).
Overview, PD, Calc, ExpandScalarProduct, ScalarProduct.
[p, q] + SPD[q] SPD
p\cdot q+q^2
[p - q, q + 2 p] SPD
(p-q)\cdot (2 p+q)
[ SPD[p - q, q + 2 p] ] Calc
-p\cdot q+2 p^2-q^2
[SPD[p - q]] ExpandScalarProduct
-2 (p\cdot q)+p^2+q^2
[a, b] // StandardForm
SPD
(*SPD[a, b]*)
[a, b] // FCI // StandardForm
SPD
(*Pair[Momentum[a, D], Momentum[b, D]]*)
[a, b] // FCI // FCE // StandardForm
SPD
(*SPD[a, b]*)
[ChangeDimension[SP[p, q], D]] // StandardForm
FCE
(*SPD[p, q]*)