GALR[mu,n,nb] denotes the perpendicular component in the lightcone decomposition of the Dirac matrix \gamma^{\mu } along the vectors n and nb. 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, GALN, GALP, GSLP, GSLN, GSLR.
GALR[\[Mu], n, nb]\bar{\gamma }^{\mu }{}_{\perp }
StandardForm[GALR[\[Mu], n, nb] // FCI]
(*DiracGamma[LightConePerpendicularComponent[LorentzIndex[\[Mu]], Momentum[n], Momentum[nb]]]*)Notice that the properties of n and nb vectors have to be set by hand before doing the actual computation
GALR[\[Mu], n, nb] . GALP[\[Nu], n, nb] // iracSimplify\text{iracSimplify}\left(\bar{\gamma }^{\mu }{}_{\perp }.\left(\frac{1}{2} \overline{\text{nb}}^{\nu } \bar{\gamma }\cdot \overline{n}\right)\right)
FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;GALR[\[Mu], n, nb] . GALP[\[Nu], n, nb] // DiracSimplify-\frac{1}{2} \overline{\text{nb}}^{\nu } \left(\bar{\gamma }\cdot \overline{n}\right).\bar{\gamma }^{\mu }{}_{\perp }
FCClearScalarProducts[]