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