FeynAmpDenominatorSimplify
FeynAmpDenominatorSimplify[exp]
tries to simplify each PropagatorDenominator
in a canonical way. FeynAmpDenominatorSimplify[exp, q1]
simplifies all FeynAmpDenominator
s in exp
in a canonical way, including momentum shifts. Scaleless integrals are discarded.
See also
Overview, TID.
Examples
FeynAmpDenominatorSimplify
The cornerstone of dimensional regularization is that ∫dnkf(k)/k4=0
FeynAmpDenominatorSimplify[f[k] FAD[k, k], k]
0
This brings some loop integrals into a standard form.
FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]], k]
k2.(k−p1+p2)21
FeynAmpDenominatorSimplify[FAD[k, k, k - q], k]
(k2)2.(k−q)21
FeynAmpDenominatorSimplify[f[k] FAD[k, k - q, k - q], k]
(k2)2.(k−q)2f(q−k)
FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]] SPD[k, k], k]
ApartFF[%, {k}]
TID[%, k] // Factor2
k2.(k−p1+p2)22(k⋅p2)+k2+p22
k2.(k−p1+p2)22(k⋅p2)+p22
k2.(k−p1+p2)2p1⋅p2
FDS[FAD[k - p1, k - p2] SPD[k, OPEDelta]^2, k]
k2.(k−p1+p2)2(k⋅Δ+Δ⋅p2)2