GSLPD[p,n,nb] denotes the positive component in the
lightcone decomposition of the slashed Dirac matrix (\gamma \cdot p) along the vectors
n and nb in D
dimensions. It corresponds to \frac{1}{2}
(\bar{n} \cdot p) (\gamma \cdot n).
If one omits n and nb, the program will use
default vectors specified via $FCDefaultLightconeVectorN
and $FCDefaultLightconeVectorNB.
Overview, DiracGamma, GALPD, GALND, GALRD, GSLND, GSLRD.
GSLPD[p, n, nb]\frac{1}{2} \gamma \cdot n (\text{nb}\cdot p)
StandardForm[GSLPD[p, n, nb] // FCI]\frac{1}{2} \;\text{DiracGamma}[\text{Momentum}[n,D],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
GSLPD[p, n, nb] . GSLPD[q, n, nb] // DiracSimplify\frac{1}{4} n^2 (\text{nb}\cdot p) (\text{nb}\cdot q)
FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;GSLPD[p, n, nb] . GSLPD[q, n, nb] // DiracSimplify0
FCClearScalarProducts[]