FeynCalc manual (development version)

ThreeDivergence

ThreeDivergence[exp, CV[p, i]] calculates the partial derivative of exp w.r.t. p^i.

ThreeDivergence[exp, CV[p, i], CV[p,i], ...] gives the multiple derivative.

Owing to the fact that in FeynCalc dummy Cartesian index are always understood to be upper indices, applying ThreeDivergence to an expression is equivalent to the action of \nabla^i = \frac{\partial}{\partial p^i}.

See also

Overview, FourDivergence.

Examples

CSP[p, q] 
 
ThreeDivergence[%, CV[q, i]]

\overline{p}\cdot \overline{q}

\overline{p}^i

CSP[p - k, q] 
 
ThreeDivergence[%, CV[k, i]]

(\overline{p}-\overline{k})\cdot \overline{q}

-\overline{q}^i

CFAD[{p, m^2}, p - q] 
 
ThreeDivergence[%, CVD[p, i]]

\frac{1}{(p^2+m^2-i \eta ).((p-q)^2-i \eta )}

\frac{2 q^i-2 p^i}{(p^2+m^2-i \eta ).((p-q)^2-i \eta )^2}-\frac{2 p^i}{(p^2+m^2-i \eta )^2.((p-q)^2-i \eta )}

Differentiation of 3-vectors living in different dimensions (3, D-1, D-4) works only in the t’Hooft-Veltman scheme

ThreeDivergence[CVD[p, i], CV[p, j]]

1h9o7vmxcyb17

\text{\$Aborted}

FCSetDiracGammaScheme["BMHV"];
ThreeDivergence[CVD[p, i], CV[p, j]]

\bar{\delta }^{ij}