MTLPD[mu,nu,n,nb] denotes the positive component in the lightcone decomposition of the metric tensor g^{\mu \nu} along the vectors n and nb. It corresponds to \frac{1}{2} \bar{n}^{\mu} n^\nu.
If one omits n and nb, the program will use default vectors specified via $FCDefaultLightconeVectorN and $FCDefaultLightconeVectorNB.
Overview, Pair, FVLPD, FVLND, FVLRD, SPLPD, SPLND, SPLRD, MTLND, MTLRD.
MTLPD[\[Mu], \[Nu], n, nb]\frac{n^{\nu } \;\text{nb}^{\mu }}{2}
StandardForm[MTLPD[\[Mu], \[Nu], n, nb] // FCI]\frac{1}{2} \;\text{Pair}[\text{LorentzIndex}[\mu ,D],\text{Momentum}[\text{nb},D]] \;\text{Pair}[\text{LorentzIndex}[\nu ,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
MTLPD[\[Mu], \[Nu], n, nb] FVD[p, \[Mu]] // Contract\frac{1}{2} n^{\nu } (\text{nb}\cdot p)
MTLPD[\[Mu], \[Nu], n, nb] FVD[p, \[Nu]] // Contract\frac{1}{2} \;\text{nb}^{\mu } (n\cdot p)
MTLPD[\[Mu], \[Nu], n, nb] FVD[n, \[Nu]] // Contract\frac{n^2 \;\text{nb}^{\mu }}{2}
FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;MTLPD[\[Mu], \[Nu], n, nb] FVD[n, \[Nu]] // Contract0
FCClearScalarProducts[]