FeynCalc manual (development version)

 

SPD

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).

See also

Overview, PD, Calc, ExpandScalarProduct, ScalarProduct.

Examples

SPD[p, q] + SPD[q]

p\cdot q+q^2

SPD[p - q, q + 2 p]

(p-q)\cdot (2 p+q)

Calc[ SPD[p - q, q + 2 p] ]

-p\cdot q+2 p^2-q^2

ExpandScalarProduct[SPD[p - q]]

-2 (p\cdot q)+p^2+q^2

SPD[a, b] // StandardForm

(*SPD[a, b]*)
SPD[a, b] // FCI // StandardForm

(*Pair[Momentum[a, D], Momentum[b, D]]*)
SPD[a, b] // FCI // FCE // StandardForm

(*SPD[a, b]*)
FCE[ChangeDimension[SP[p, q], D]] // StandardForm

(*SPD[p, q]*)