FourDivergence
FourDivergence[exp, FV[p, mu]]
calculates the partial derivative of exp w.r.t pμ. FourDivergence[exp, FV[p, mu], FV[p,nu], ...]
gives the multiple derivative.
See also
Overview, ThreeDivergence.
Examples
SP[p, q]
FourDivergence[%, FV[q, \[Mu]]]
p⋅q
pμ
SP[p - k, q]
FourDivergence[%, FV[k, \[Mu]]]
(p−k)⋅q
−qμ
SFAD[{p, m^2}]
FourDivergence[%, FVD[p, \[Nu]]]
(p2−m2+iη)1
−(p2−m2+iη)22pν
FVD[l, \[Mu]] FAD[{l, 0}, {l - p, 0}]
FourDivergence[%, FVD[l, \[Mu]]]
l2.(l−p)2lμ
l2.(l−p)2D−(l2)2.(l−p)22l2+l2.(l−p)42(l⋅p)−2l2
SP[p, w]*SpinorUBar[p2, m] . GS[w] . SpinorU[p1, m]
FourDivergence[%, FV[w, a]]
(p⋅w)uˉ(p2,m).(γˉ⋅w).u(p1,m)
(p⋅w)(φ(p2,m)).γˉa.(φ(p1,m))+pa(φ(p2,m)).(γˉ⋅w).(φ(p1,m))
Differentiation of 4-vectors living in different dimensions (4, D, D−4) works only in the t’Hooft-Veltman scheme
FourDivergence[FVD[p, mu], FV[p, nu]]
![0n13hj2mmcy3r](img/0n13hj2mmcy3r.svg)
$Aborted
FCSetDiracGammaScheme["BMHV"];
FourDivergence[FVD[p, mu], FV[p, nu]]
gˉmunu