FeynCalc manual (development version)

MTLRD

MTLRD[p,mu,n,nb] denotes the perpendicular component in the lightcone decomposition of the metric tensor g^{\mu \nu} along the vectors n and nb in D dimensions. It corresponds to g^{\mu \nu}_{\perp}.

If one omits n and nb, the program will use default vectors specified via $FCDefaultLightconeVectorN and $FCDefaultLightconeVectorNB.

See also

Overview, Pair, FVLND, FVLPD, SPLPD, SPLND, SPLRD, MTLPD, MTLND.

Examples

MTLRD[\[Mu], \[Nu], n, nb]

g^{\mu \nu }{}_{\perp }

MTLRD[\[Mu], \[Nu], n, nb] // FCI // StandardForm

(*Pair[LightConePerpendicularComponent[LorentzIndex[\[Mu], D], Momentum[n, D], Momentum[nb, D]], LightConePerpendicularComponent[LorentzIndex[\[Nu], D], Momentum[n, D], Momentum[nb, D]]]*)
MTLRD[\[Mu], \[Nu], n, nb] FVD[p, \[Mu]] // Contract

p^{\nu }{}_{\perp }

MTLRD[\[Mu], \[Nu], n, nb] FVLPD[q, \[Mu], n, nb] // Contract

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