FeynCalc manual (development version)

SP

SP[a, b] denotes a 4-dimensional scalar product. SP[a, b] is transformed into ScalarProduct[a, b] by FeynCalcInternal.

SP[p] is the same as SP[p, p] (=p^2).

See also

Overview, Calc, ExpandScalarProduct, ScalarProduct.

Examples

SP[p, q] + SP[q]

\overline{p}\cdot \overline{q}+\overline{q}^2

SP[p - q, q + 2 p]

(\overline{p}-\overline{q})\cdot (2 \overline{p}+\overline{q})

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

-\overline{p}\cdot \overline{q}+2 \overline{p}^2-\overline{q}^2

ExpandScalarProduct[SP[p - q]]

-2 \left(\overline{p}\cdot \overline{q}\right)+\overline{p}^2+\overline{q}^2

SP[a, b] // StandardForm

(*SP[a, b]*)

SP[a, b] // FCI // StandardForm

(*Pair[Momentum[a], Momentum[b]]*)

SP[a, b] // FCI // FCE // StandardForm

(*SP[a, b]*)