SFAD[{{q1 +..., p1 . q2 +...,} {m^2, s}, n}, ...]
denotes a standard Lorentzian propagator given by \frac{1}{[(q_1+\ldots)^2 + p_1 \cdot q_2 ... + m^2 +
s i \eta]^n}, where q_1^2 and
p_1 \cdot q_2 are Lorentzian scalar
products in D dimensions.
For brevity one can also use shorter forms such as
SFAD[{q1+ ..., m^2}, ...],
SFAD[{q1+ ..., m^2 , n}, ...],
SFAD[{q1+ ..., {m^2, -1}}, ...], SFAD[q1,...]
etc.
If s is not explicitly specified, its value is
determined by the option EtaSign, which has the default
value +1 and corresponds to + i
\eta
If n is not explicitly specified, then the default value
1 is assumed. Translation into the FeynCalc internal form
is performed by FeynCalcInternal, where an
SFAD is encoded using the special head
StandardPropagatorDenominator.
SFAD can represent more versatile propagators as
compared to the old FAD. In particular, FAD
does not allow one to enter eikonal propagators, track the sign of the
i \eta or change the sign and the form
of the mass term.
SFAD[{{p, 0}, m^2}]\frac{1}{(p^2-m^2+i \eta )}
SFAD[{{p, 0}, {m^2, -1}}]\frac{1}{(p^2-m^2-i \eta )}
SFAD[{{p, 0}, {-m^2, -1}}]\frac{1}{(p^2+m^2-i \eta )}
SFAD[{{0, p . q}, m^2}]\frac{1}{(p\cdot q-m^2+i \eta )}
SFAD[{{0, n . q}}]\frac{1}{(n\cdot q+i \eta )}
SFAD[{{p, p . q}, m^2}]\frac{1}{(p^2+p\cdot q-m^2+i \eta )}
The so called Smirnov-notation for propagators can be achieved by
multiplying the quadratic part by I and switching the sign
of the mass term.
SFAD[{{I*p, 0}, -m^2}]\frac{1}{(-p^2+m^2+i \eta )}
If one wants to have additional variables multiplying loop or
external momenta, those need to be declared to be of the
FCVariable type
DataType[la, FCVariable] = True\text{True}
SFAD[{{0, la p . q}, m^2}]\frac{1}{(\text{la} (p\cdot q)-m^2+i \eta )}
% // FCI // StandardForm
(*FeynAmpDenominator[StandardPropagatorDenominator[0, la Pair[Momentum[p, D], Momentum[q, D]], -m^2, {1, 1}]]*)