SPLN[p,q,n,nb] denotes the negative component in the
lightcone decomposition of the scalar product p \cdot q along the vectors n
and nb. It corresponds to \frac{1}{2} (p \cdot \bar{n}) (q \cdot
n).
If one omits n and nb, the program will use
default vectors specified via $FCDefaultLightconeVectorN
and $FCDefaultLightconeVectorNB.
Overview, Pair, FVLN, FVLP, FVLR, SPLP, SPLR, MTLP, MTLN, MTLR.
SPLN[p, q, n, nb]\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{\text{nb}}\cdot \overline{p}\right)
StandardForm[SPLN[p, q, n, nb] // FCI]\frac{1}{2} \;\text{Pair}[\text{Momentum}[n],\text{Momentum}[q]] \;\text{Pair}[\text{Momentum}[\text{nb}],\text{Momentum}[p]]
Notice that the properties of n and nb
vectors have to be set by hand before doing the actual computation
SPLN[p1 + p2 + n, q, n, nb] // ExpandScalarProduct\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{n}\cdot \overline{\text{nb}}+\overline{\text{nb}}\cdot \overline{\text{p1}}+\overline{\text{nb}}\cdot \overline{\text{p2}}\right)
FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;SPLN[p1 + p2 + n, q, n, nb] // ExpandScalarProduct\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{\text{nb}}\cdot \overline{\text{p1}}+\overline{\text{nb}}\cdot \overline{\text{p2}}+2\right)
FCClearScalarProducts[]