FeynCalc manual (development version)

 

MTLP

MTLP[mu,nu,n,nb] denotes the positive component in the lightcone decomposition of the metric tensor gμνg^{\mu \nu} along the vectors n and nb. It corresponds to 12nˉμnν\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.

See also

Overview, Pair, FVLP, FVLN, FVLR, SPLP, SPLN, SPLR, MTLN, MTLR.

Examples

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

12nνnbμ\frac{1}{2} \overline{n}^{\nu } \overline{\text{nb}}^{\mu }

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

12  Pair[LorentzIndex[μ],Momentum[nb]]  Pair[LorentzIndex[ν],Momentum[n]]\frac{1}{2} \;\text{Pair}[\text{LorentzIndex}[\mu ],\text{Momentum}[\text{nb}]] \;\text{Pair}[\text{LorentzIndex}[\nu ],\text{Momentum}[n]]

Notice that the properties of n and nb vectors have to be set by hand before doing the actual computation

MTLP[\[Mu], \[Nu], n, nb] FV[p, \[Mu]] // Contract

12nν(nbp)\frac{1}{2} \overline{n}^{\nu } \left(\overline{\text{nb}}\cdot \overline{p}\right)

MTLP[\[Mu], \[Nu], n, nb] FV[p, \[Nu]] // Contract

12nbμ(np)\frac{1}{2} \overline{\text{nb}}^{\mu } \left(\overline{n}\cdot \overline{p}\right)

MTLP[\[Mu], \[Nu], n, nb] FV[n, \[Nu]] // Contract

12n2nbμ\frac{1}{2} \overline{n}^2 \overline{\text{nb}}^{\mu }

FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;
MTLP[\[Mu], \[Nu], n, nb] FV[n, \[Nu]] // Contract

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FCClearScalarProducts[]