GALP[mu,n,nb] denotes the positive component in the
lightcone decomposition of the Dirac matrix \gamma^{\mu } along the vectors
n and nb. It corresponds to \frac{1}{2} \bar{n}^{\mu} (\gamma \cdot
n).
If one omits n and nb, the program will use
default vectors specified via $FCDefaultLightconeVectorN
and $FCDefaultLightconeVectorNB.
Overview, DiracGamma, GALN, GALR, GSLP, GSLN, GSLR.
GALP[\[Mu], n, nb]\frac{1}{2} \overline{\text{nb}}^{\mu } \bar{\gamma }\cdot \overline{n}
StandardForm[GALP[\[Mu], n, nb] // FCI]\frac{1}{2} \;\text{DiracGamma}[\text{Momentum}[n]] \;\text{Pair}[\text{LorentzIndex}[\mu ],\text{Momentum}[\text{nb}]]
Notice that the properties of n and nb
vectors have to be set by hand before doing the actual computation
GALP[\[Mu], n, nb] . GALP[\[Nu], n, nb] // DiracSimplify\frac{1}{4} \overline{n}^2 \overline{\text{nb}}^{\mu } \overline{\text{nb}}^{\nu }
FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;GALP[\[Mu], n, nb] . GALP[\[Nu], n, nb] // DiracSimplify0
FCClearScalarProducts[]