FeynCalc manual (development version)

 

GSLND

GSLND[p,n,nb] denotes the negative component in the lightcone decomposition of the slashed Dirac matrix (\gamma \cdot p) along the vectors n and nb in D dimensions. It corresponds to \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]

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

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

\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

\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

0

FCClearScalarProducts[]