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