FeynCalc manual (development version)

SPLPD

SPLPD[p,q,n,nb] denotes the positive 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 n) (q \cdot \bar{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, SPLND, SPLRD, MTLPD, MTLND, MTLRD.

Examples

SPLPD[p, q, n, nb]

\frac{1}{2} (n\cdot p) (\text{nb}\cdot q)

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

\frac{1}{2} \;\text{Pair}[\text{Momentum}[n,D],\text{Momentum}[p,D]] \;\text{Pair}[\text{Momentum}[\text{nb},D],\text{Momentum}[q,D]]

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

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

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

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

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

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

FCClearScalarProducts[]