FeynCalc manual (development version)

Apart2

Apart2[expr] partial fractions propagators of the form 1/[(q2m12)(q2m22)]1/[(q^2-m1^2)(q^2-m2^2)].

See also

Overview, FAD, FeynAmpDenominator, ApartFF.

Examples

FAD[{q, m}, {q, M}, q - p] 
 
Apart2[%] 
 
StandardForm[FCE[%]]

1(q2m2).(q2M2).(qp)2\frac{1}{\left(q^2-m^2\right).\left(q^2-M^2\right).(q-p)^2}

1(q2m2).(qp)21(q2M2).(qp)2m2M2\frac{\frac{1}{\left(q^2-m^2\right).(q-p)^2}-\frac{1}{\left(q^2-M^2\right).(q-p)^2}}{m^2-M^2}

FAD[{q,m},p+q]FAD[{q,M},p+q]m2M2\frac{\text{FAD}[\{q,m\},-p+q]-\text{FAD}[\{q,M\},-p+q]}{m^2-M^2}

Apart2 can also handle Cartesian propagators with square roots. To disable this mode use textSqrttotextFalsetext{Sqrt}to text{False}

int = CFAD[{{k, 0}, {+m^2, -1}, 1}, {{k - p, 0}, {0, -1}, 1}] GFAD[{{DE - Sqrt[CSPD[k, k]], 1}, 1}] 
 
int // FeynAmpDenominatorCombine // Apart2

1(DEk2+iη)(k2+m2iη).((kp)2iη)\frac{1}{(\text{DE}-\sqrt{k^2}+i \eta ) (k^2+m^2-i \eta ).((k-p)^2-i \eta )}

DE(k2+m2iη).((kp)2iη)+1(DEk2+iη).((kp)2iη)+k2(k2+m2iη).((kp)2iη)DE2+m2\frac{\frac{\text{DE}}{(k^2+m^2-i \eta ).((k-p)^2-i \eta )}+\frac{1}{(\text{DE}-\sqrt{k^2}+i \eta ).((k-p)^2-i \eta )}+\frac{\sqrt{k^2}}{(k^2+m^2-i \eta ).((k-p)^2-i \eta )}}{\text{DE}^2+m^2}