FeynCalc manual (development version)

SPLRD

SPLRD[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, FVLND, FVLPD, FVLRD, SPLPD, SPLND, MTLPD, MTLND, MTLRD.

Examples

SPLRD[p, q, n, nb]

p\cdot q_{\perp }

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

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

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

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

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

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

\text{p1}\cdot q_{\perp }+\text{p2}\cdot q_{\perp }