FeynCalc manual (development version)

GFAD

GFAD[{{{x, s}, n}, ...] denotes a generic propagator given by 1[x+siη]n\frac{1}{[x + s i \eta]^n}, where x can be an arbitrary expression. For brevity one can also use shorter forms such as GFAD[{x, n}, ...], GFAD[{x}, ...] or GFAD[x, ...].

If s is not explicitly specified, then its value is determined by the option EtaSign, which has the default value +1.

If n is not explicitly specified, then the default value 1 is assumed. Translation into FeynCalc internal form is performed by FeynCalcInternal, where a GFAD is encoded using the special head GenericPropagatorDenominator.

See also

Overview, FAD, SFAD, CFAD.

Examples

GFAD[2 z SPD[p1, q] SPD[p2, q] + x SPD[p1, p2]] 
 
FeynAmpDenominatorExplicit[%] 
 
% // FCE // StandardForm

1(x(p1⋅  p2)+2z(p1⋅q)(p2⋅q)+iη)\frac{1}{(x (\text{p1}\cdot \;\text{p2})+2 z (\text{p1}\cdot q) (\text{p2}\cdot q)+i \eta )}

12z(p1⋅q)(p2⋅q)+x(p1⋅  p2)\frac{1}{2 z (\text{p1}\cdot q) (\text{p2}\cdot q)+x (\text{p1}\cdot \;\text{p2})}

1x  SPD[p1,p2]+2z  SPD[p1,q]  SPD[p2,q]\frac{1}{x \;\text{SPD}[\text{p1},\text{p2}]+2 z \;\text{SPD}[\text{p1},q] \;\text{SPD}[\text{p2},q]}