FeynCalc manual (development version)

CSP

CSP[p, q] is the 3-dimensional scalar product of p with q and is transformed into CartesianPair[CartesianMomentum[p],CartesianMomentum[q]] by FeynCalcInternal.

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

See also

Overview, SP, ScalarProduct, CartesianScalarProduct.

Examples

CSP[p, q] + CSP[q]

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

CSP[p - q, q + 2 p]

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

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

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

ExpandScalarProduct[CSP[p - q]]

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

CSP[a, b] // StandardForm

(*CSP[a, b]*)

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

(*CartesianPair[CartesianMomentum[a], CartesianMomentum[b]]*)

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

(*CSP[a, b]*)