GALND[mu,n,nb] denotes the negative component in the
lightcone decomposition of the Dirac matrix \gamma^{\mu } along the vectors
n and nb in D-dimensions. 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, GALPD, GALRD, GSLPD, GSLND, GSLRD.
GALND[\[Mu], n, nb]\frac{1}{2} n^{\mu } \gamma \cdot \;\text{nb}
StandardForm[GALND[\[Mu], n, nb] // FCI]\frac{1}{2} \;\text{DiracGamma}[\text{Momentum}[\text{nb},D],D] \;\text{Pair}[\text{LorentzIndex}[\mu ,D],\text{Momentum}[n,D]]
Notice that the properties of n and nb
vectors have to be set by hand before doing the actual computation
GALND[\[Mu], n, nb] . GALND[\[Nu], n, nb] // DiracSimplify\frac{1}{4} \;\text{nb}^2 n^{\mu } n^{\nu }
FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;GALND[\[Mu], n, nb] . GALND[\[Nu], n, nb] // DiracSimplify0
FCClearScalarProducts[]