FeynCalc manual (development version)

SPLND

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.

See also

Overview, Pair, FVLND, FVLPD, FVLRD, SPLPD, SPLRD, MTLPD, MTLND, MTLRD.

Examples

SPLND[p, q, n, nb]

\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

SPLND[p1 + p2 + n, q, n, nb] // ExpandScalarProduct

\frac{1}{2} (n\cdot q) (n\cdot \;\text{nb}+\text{nb}\cdot \;\text{p1}+\text{nb}\cdot \;\text{p2})

FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;

SPLND[p1 + p2 + n, q, n, nb] // ExpandScalarProduct

\frac{1}{2} (n\cdot q) (\text{nb}\cdot \;\text{p1}+\text{nb}\cdot \;\text{p2}+2)

FCClearScalarProducts[]