FeynCalc manual (development version)

ToGFAD

ToGFAD[exp] converts all occurring propagator types (FAD, SFAD, CFAD) to GFADs. This is mainly useful when doing expansions in kinematic invariants, where e.g. scalar products may not be appear explicitly when using FAD- or SFAD-notation.

ToGFAD is the inverse operation to FromGFAD.

Using the option “OnlyMixedQuadraticEikonalPropagators” one can limit the conversion to a particular type of standard and Cartesian propagator denominators that contain both quadratic and eikonal pieces. Those are the ones that usually cause issues when doing topology minimization

Examples

ToGFAD[FAD[p]]

\frac{1}{(p^2+i \eta )}

ToGFAD[FAD[p]] // StandardForm

(*FeynAmpDenominator[GenericPropagatorDenominator[Pair[Momentum[p, D], Momentum[p, D]], {1, 1}]]*)

ToGFAD[SFAD[{p + q, m^2}]]

\frac{1}{(-m^2+p^2+2 (p\cdot q)+q^2+i \eta )}

ToGFAD[SFAD[{p + q, m^2}]] // StandardForm

(*FeynAmpDenominator[GenericPropagatorDenominator[-m^2 + Pair[Momentum[p, D], Momentum[p, D]] + 2 Pair[Momentum[p, D], Momentum[q, D]] + Pair[Momentum[q, D], Momentum[q, D]], {1, 1}]]*)

ToGFAD[SFAD[{p + q, m^2}], FinalSubstitutions -> {SPD[q] -> 0}]

\frac{1}{(-m^2+p^2+2 (p\cdot q)+i \eta )}

ToGFAD[SFAD[{p + q, m^2}], FinalSubstitutions -> {SPD[q] -> 0}] // StandardForm

(*FeynAmpDenominator[GenericPropagatorDenominator[-m^2 + Pair[Momentum[p, D], Momentum[p, D]] + 2 Pair[Momentum[p, D], Momentum[q, D]], {1, 1}]]*)

This is not a mixed quadratic-eikonal propagator so it remains unchanged

ToGFAD[SFAD[{{k2, 0}, {0, 1}, 1}], "OnlyMixedQuadraticEikonalPropagators" -> True, 
   FCE -> True] // StandardForm

(*SFAD[{{k2, 0}, {0, 1}, 1}]*)

This is a mixed propagator that will be converted to a GFAD

ToGFAD[SFAD[{{k1, 2 gkin meta k1 . n - 2 gkin meta u0b k1 . n - meta u0b k1 . nb}, 
     {2 gkin meta^2 u0b - 2 gkin meta^2 u0b^2, 1}, 1}], 
   "OnlyMixedQuadraticEikonalPropagators" -> True, FCE -> True] // StandardForm

(*GFAD[{{-2 gkin meta^2 u0b + 2 gkin meta^2 u0b^2 + SPD[k1, k1] + 2 gkin meta SPD[k1, n] - 2 gkin meta u0b SPD[k1, n] - meta u0b SPD[k1, nb], 1}, 1}]*)

ToGFAD

See also

Examples