FeynCalc manual (development version)

FAD

FAD is the FeynCalc external form of FeynAmpDenominator and denotes an inverse propagator.

FAD[q, q-p, ...] is 1q2(qp)2\frac{1}{q^2 (q-p)^2 \ldots}.

FAD[{q1,m}, {q1-p,m}, q2, ...] is 1[q12m2][(q1p)2m2]q22\frac{1}{[q1^2 - m^2][(q1-p)^2 - m^2] q2^2}. Translation into FeynCalc internal form is performed by FeynCalcInternal.

See also

Overview, FAD, FCE, FCI, FeynAmpDenominator, FeynAmpDenominatorSimplify, PropagatorDenominator.

Examples

FAD[q, p - q]

1q2.(pq)2\frac{1}{q^2.(p-q)^2}

FAD[p, {p - q, m}]

1p2.((pq)2m2)\frac{1}{p^2.\left((p-q)^2-m^2\right)}

FAD[{p, 0, 2}, {p - q, m, 3}]

1(p2)2.((pq)2m2)3\frac{1}{\left(p^2\right)^2.\left((p-q)^2-m^2\right)^3}

FAD[q, p - q] // FCI // StandardForm

(*FeynAmpDenominator[PropagatorDenominator[Momentum[q, D], 0], PropagatorDenominator[Momentum[p, D] - Momentum[q, D], 0]]*)
FAD[p] FAD[p - q] // FeynAmpDenominatorCombine[#, FCE -> True] & // StandardForm

(*FAD[p, p - q]*)