GALRD[mu,n,nb] denotes the perpendicular component in the lightcone decomposition of the Dirac matrix \gamma^{\mu } along the vectors n and nb in D dimensions. It corresponds to \gamma^{\mu}_{\perp}.
If one omits n and nb, the program will use default vectors specified via $FCDefaultLightconeVectorN and $FCDefaultLightconeVectorNB.
Overview, DiracGamma, GALND, GALPD, GSLPD, GSLND, GSLRD.
GALRD[\[Mu], n, nb]\gamma ^{\mu }{}_{\perp }
StandardForm[GALRD[\[Mu], n, nb] // FCI]
(*DiracGamma[LightConePerpendicularComponent[LorentzIndex[\[Mu], D], Momentum[n, D], Momentum[nb, D]], D]*)Notice that the properties of n and nb vectors have to be set by hand before doing the actual computation
GALRD[\[Mu], n, nb] . GALPD[\[Nu], n, nb] // DiracSimplify-\frac{1}{4} \;\text{nb}^{\nu } (n\cdot \;\text{nb}) (\gamma \cdot n).\gamma ^{\mu }{}_{\perp }-\frac{1}{4} n^2 \;\text{nb}^{\nu } (\gamma \cdot \;\text{nb}).\gamma ^{\mu }{}_{\perp }
FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;GALRD[\[Mu], n, nb] . GALPD[\[Nu], n, nb] // DiracSimplify-\frac{1}{2} \;\text{nb}^{\nu } (\gamma \cdot n).\gamma ^{\mu }{}_{\perp }
FCClearScalarProducts[]