FeynCalc manual (development version)

 

GSLN

GSLN[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. 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, GALP, GALN, GALR, GSLP, GSLR.

Examples

GSLN[p, n, nb]

12(np)γˉnb\frac{1}{2} \left(\overline{n}\cdot \overline{p}\right) \bar{\gamma }\cdot \overline{\text{nb}}

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

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

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

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

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

FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;
GSLN[p, n, nb] . GSLN[q, n, nb] // DiracSimplify

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FCClearScalarProducts[]