GSLP[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. 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, GALP, GALN, GALR, GSLN, GSLR.
GSLP[p, n, nb]\frac{1}{2} \bar{\gamma }\cdot \overline{n} \left(\overline{\text{nb}}\cdot \overline{p}\right)
StandardForm[GSLP[p, n, nb] // FCI]\frac{1}{2} \;\text{DiracGamma}[\text{Momentum}[n]] \;\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
GSLP[p, n, nb] . GSLP[q, n, nb] // DiracSimplify\frac{1}{4} \overline{n}^2 \left(\overline{\text{nb}}\cdot \overline{p}\right) \left(\overline{\text{nb}}\cdot \overline{q}\right)
FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;GSLP[p, n, nb] . GSLP[q, n, nb] // DiracSimplify0
FCClearScalarProducts[]