FeynCalc manual (development version)

FeynAmpDenominatorSimplify

FeynAmpDenominatorSimplify[exp] tries to simplify each PropagatorDenominator in a canonical way. FeynAmpDenominatorSimplify[exp, q1] simplifies all FeynAmpDenominators in exp in a canonical way, including momentum shifts. Scaleless integrals are discarded.

See also

Overview, TID.

Examples

FDS

FeynAmpDenominatorSimplify\text{FeynAmpDenominatorSimplify}

The cornerstone of dimensional regularization is that dnkf(k)/k4=0\int d^n k f(k)/k^4 = 0

FeynAmpDenominatorSimplify[f[k] FAD[k, k], k]

00

This brings some loop integrals into a standard form.

FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]], k]

1k2.(kp1+p2)2\frac{1}{k^2.(k-p_1+p_2){}^2}

FeynAmpDenominatorSimplify[FAD[k, k, k - q], k]

1(k2)2.(kq)2\frac{1}{\left(k^2\right)^2.(k-q)^2}

FeynAmpDenominatorSimplify[f[k] FAD[k, k - q, k - q], k]

f(qk)(k2)2.(kq)2\frac{f(q-k)}{\left(k^2\right)^2.(k-q)^2}

FeynAmpDenominatorSimplify[FAD[k - Subscript[p, 1], k - Subscript[p, 2]] SPD[k, k], k] 
 
ApartFF[%, {k}] 
 
TID[%, k] // Factor2

2(kp2)+k2+p22k2.(kp1+p2)2\frac{2 \left(k\cdot p_2\right)+k^2+p_2{}^2}{k^2.(k-p_1+p_2){}^2}

2(kp2)+p22k2.(kp1+p2)2\frac{2 \left(k\cdot p_2\right)+p_2{}^2}{k^2.(k-p_1+p_2){}^2}

p1p2k2.(kp1+p2)2\frac{p_1\cdot p_2}{k^2.(k-p_1+p_2){}^2}

FDS[FAD[k - p1, k - p2] SPD[k, OPEDelta]^2, k]

(kΔ+Δ  p2)2k2.(kp1+p2)2\frac{(k\cdot \Delta +\Delta \cdot \;\text{p2})^2}{k^2.(k-\text{p1}+\text{p2})^2}