FeynCalc manual (development version)

 

SPLR

SPLR[p,q,n,nb] denotes the perpendicular component in the lightcone decomposition of the scalar product p \cdot q along the vectors n and nb. It corresponds to (p \cdot q)_{\perp}.

If one omits n and nb, the program will use default vectors specified via $FCDefaultLightconeVectorN and $FCDefaultLightconeVectorNB.

See also

Overview, Pair, FVLN, FVLP, FVLR, SPLP, SPLN, MTLP, MTLN, MTLR.

Examples

SPLR[p, q, n, nb]

\overline{p}\cdot \overline{q}_{\perp }

StandardForm[SPLR[p, q, n, nb] // FCI]

(*Pair[LightConePerpendicularComponent[Momentum[p], Momentum[n], Momentum[nb]], LightConePerpendicularComponent[Momentum[q], Momentum[n], Momentum[nb]]]*)

Notice that the properties of n and nb vectors have to be set by hand before doing the actual computation

SPLR[p1 + p2, q1 + q2, n, nb] // FCI // ExpandScalarProduct

\overline{\text{p1}}\cdot \overline{\text{q1}}_{\perp }+\overline{\text{p1}}\cdot \overline{\text{q2}}_{\perp }+\overline{\text{p2}}\cdot \overline{\text{q1}}_{\perp }+\overline{\text{p2}}\cdot \overline{\text{q2}}_{\perp }

SPLR[p1 + p2 + n, q, n, nb] // FCI // ExpandScalarProduct

\overline{\text{p1}}\cdot \overline{q}_{\perp }+\overline{\text{p2}}\cdot \overline{q}_{\perp }