OneLoopSimplify
OneLoopSimplify[amp, q]
simplifies the one-loop amplitude amp. The second argument denotes the integration momentum.
If the first argument has head FeynAmp
then OneLoopSimplify[FeynAmp[name, k, expr], k]
transforms to OneLoopSimplify[expr, k]
See also
Overview, TID, TIDL.
Examples
SPD[k, r] FAD[{k, m} , k - p] // FCI
OneLoopSimplify[%, k]
OneLoopSimplify[% /. m -> 0, k]
(k2−m2).(k−p)2k⋅r
2p2k2.((k−p)2−m2)(m2+p2)(p⋅r)−2p2(k2−m2)p⋅r
2k2.(k−p)2p⋅r
FAD[k, k, k - Subscript[p, 1], k - Subscript[p, 2]] FVD[k, \[Mu]] // FCI
OneLoopSimplify[ %, k]
FCE[%] /. SPD[Subscript[p, 1]] -> 0 // FCI
(k2)2.(k−p1)2.(k−p2)2kμ
2(k2)2.(k−p1)2((p1⋅p2)2−p12p22)p12p2μ−p1μ(p1⋅p2)+2(k2)2.(k−p1)2.(k−p2)2((p1⋅p2)2−p12p22)−p12p22p1μ−p12p22p2μ+p12p2μ(p1⋅p2)+p22p1μ(p1⋅p2)−2(k2)2.(k−p2)2((p1⋅p2)2−p12p22)p2μ(p1⋅p2)−p22p1μ−2k2.(k−p1)2.(k−p2)2((p1⋅p2)2−p12p22)p12p2μ+p22p1μ−p1μ(p1⋅p2)−p2μ(p1⋅p2)
2(p1⋅p2)(k2)2.(k−p1)2.(k−p2)2p22p1μ−2(p1⋅p2)(k2)2.(k−p1)2p1μ−2(k2)2.(k−p2)2(p1⋅p2)2p2μ(p1⋅p2)−p22p1μ−2k2.(k−p1)2.(k−p2)2(p1⋅p2)2p22p1μ−p1μ(p1⋅p2)−p2μ(p1⋅p2)
OneLoopSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]] SPD[k, l]^2, k]
−4(1−D)k2.(k−p1+p2)2D(l⋅p1)2+D(l⋅p2)2+2D(l⋅p2)(l⋅p1)−l2p12−l2p22−4(l⋅p2)(l⋅p1)+2l2(p1⋅p2)