SPLND[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
in D-dimensions. 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, FVLND, FVLPD, FVLRD, SPLPD, SPLRD, MTLPD, MTLND, MTLRD.
[p, q, n, nb] SPLND
\frac{1}{2} (n\cdot q) (\text{nb}\cdot p)
StandardForm[SPLND[p, q, n, nb] // FCI]
\frac{1}{2} \;\text{Pair}[\text{Momentum}[n,D],\text{Momentum}[q,D]] \;\text{Pair}[\text{Momentum}[\text{nb},D],\text{Momentum}[p,D]]
Notice that the properties of n
and nb
vectors have to be set by hand before doing the actual computation
[p1 + p2 + n, q, n, nb] // ExpandScalarProduct SPLND
\frac{1}{2} (n\cdot q) (n\cdot \;\text{nb}+\text{nb}\cdot \;\text{p1}+\text{nb}\cdot \;\text{p2})
[]
FCClearScalarProducts[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2; SPD
[p1 + p2 + n, q, n, nb] // ExpandScalarProduct SPLND
\frac{1}{2} (n\cdot q) (\text{nb}\cdot \;\text{p1}+\text{nb}\cdot \;\text{p2}+2)
[] FCClearScalarProducts