FeynCalc manual (development version)

 

SPLN

SPLN[p,q,n,nb] denotes the negative component in the lightcone decomposition of the scalar product pqp \cdot q along the vectors n and nb. It corresponds to 12(pnˉ)(qn)\frac{1}{2} (p \cdot \bar{n}) (q \cdot n).

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

See also

Overview, Pair, FVLN, FVLP, FVLR, SPLP, SPLR, MTLP, MTLN, MTLR.

Examples

SPLN[p, q, n, nb]

12(nq)(nbp)\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{\text{nb}}\cdot \overline{p}\right)

StandardForm[SPLN[p, q, n, nb] // FCI]

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

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

SPLN[p1 + p2 + n, q, n, nb] // ExpandScalarProduct

12(nq)(nnb+nbp1+nbp2)\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{n}\cdot \overline{\text{nb}}+\overline{\text{nb}}\cdot \overline{\text{p1}}+\overline{\text{nb}}\cdot \overline{\text{p2}}\right)

FCClearScalarProducts[]
SP[n] = 0;
SP[nb] = 0;
SP[n, nb] = 2;
SPLN[p1 + p2 + n, q, n, nb] // ExpandScalarProduct

12(nq)(nbp1+nbp2+2)\frac{1}{2} \left(\overline{n}\cdot \overline{q}\right) \left(\overline{\text{nb}}\cdot \overline{\text{p1}}+\overline{\text{nb}}\cdot \overline{\text{p2}}+2\right)

FCClearScalarProducts[]