FeynCalc manual (development version)

SPE

SPE[a, b] denotes a D4D-4-dimensional scalar product. SPE[a, b] is transformed into Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]] by FeynCalcInternal.

SPE[p] is the same as SPE[p,p] (=p2)(=p^2).

See also

Overview, PD, Calc, ExpandScalarProduct, ScalarProduct, SPD.

Examples

SPE[p, q] + SPE[q]

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

SPE[p - q, q + 2 p]

(p^q^)(2p^+q^)(\hat{p}-\hat{q})\cdot (2 \hat{p}+\hat{q})

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

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

ExpandScalarProduct[SPE[p - q]]

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

SPE[a, b] // StandardForm

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

(*Pair[Momentum[a, -4 + D], Momentum[b, -4 + D]]*)
SPE[a, b] // FCI // FCE // StandardForm

(*SPE[a, b]*)
FCE[ChangeDimension[SP[p, q], D - 4]] // StandardForm

(*SPE[p, q]*)