FeynCalc manual (development version)

 

GALN

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

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

See also

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

Examples

GALN[\[Mu], n, nb]

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

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

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

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

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

14nb2nμnν\frac{1}{4} \overline{\text{nb}}^2 \overline{n}^{\mu } \overline{n}^{\nu }

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

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FCClearScalarProducts[]