FeynCalc manual (development version)

 

GSLND

GSLND[p,n,nb] denotes the negative component in the lightcone decomposition of the slashed Dirac matrix (γp)(\gamma \cdot p) along the vectors n and nb in DD dimensions. It corresponds to 12(np)(γnˉ)\frac{1}{2} (n \cdot p) (\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, GALPD, GALND, GALRD, GSLPD, GSLRD.

Examples

GSLND[p, n, nb]

12(np)γ  nb\frac{1}{2} (n\cdot p) \gamma \cdot \;\text{nb}

StandardForm[GSLND[p, n, nb] // FCI]

12  DiracGamma[Momentum[nb,D],D]  Pair[Momentum[n,D],Momentum[p,D]]\frac{1}{2} \;\text{DiracGamma}[\text{Momentum}[\text{nb},D],D] \;\text{Pair}[\text{Momentum}[n,D],\text{Momentum}[p,D]]

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

GSLND[p, n, nb] . GSLND[q, n, nb] // DiracSimplify

14  nb2(np)(nq)\frac{1}{4} \;\text{nb}^2 (n\cdot p) (n\cdot q)

FCClearScalarProducts[]
SPD[n] = 0;
SPD[nb] = 0;
SPD[n, nb] = 2;
GSLND[p, n, nb] . GSLND[q, n, nb] // DiracSimplify

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FCClearScalarProducts[]