FeynCalc manual (development version)

 

GALP

GALP[mu,n,nb] denotes the positive component in the lightcone decomposition of the Dirac matrix γμ\gamma^{\mu } along the vectors n and nb. It corresponds to 12nˉμ(γn)\frac{1}{2} \bar{n}^{\mu} (\gamma \cdot n).

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

See also

Overview, DiracGamma, GALN, GALR, GSLP, GSLN, GSLR.

Examples

GALP[\[Mu], n, nb]

12nbμγˉn\frac{1}{2} \overline{\text{nb}}^{\mu } \bar{\gamma }\cdot \overline{n}

StandardForm[GALP[\[Mu], n, nb] // FCI]

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

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

GALP[\[Mu], n, nb] . GALP[\[Nu], n, nb] // DiracSimplify

14n2nbμnbν\frac{1}{4} \overline{n}^2 \overline{\text{nb}}^{\mu } \overline{\text{nb}}^{\nu }

FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;
GALP[\[Mu], n, nb] . GALP[\[Nu], n, nb] // DiracSimplify

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FCClearScalarProducts[]