FeynCalc manual (development version)

 

CFAD

CFAD[{{q1 +..., p1 . q2 +...,} {m^2, s}, n}, ...] denotes a Cartesian propagator given by 1[(q1+)2+p1q2...+m2+siη]n\frac{1}{[(q_1+\ldots)^2 + p_1 \cdot q_2 ... + m^2 + s i \eta]^n}, where q12q_1^2 and p1q2p_1 \cdot q_2 are Cartesian scalar products in D1D-1 dimensions.

For brevity one can also use shorter forms such as CFAD[{q1+ ..., m^2}, ...], CFAD[{q1+ ..., m^2 , n}, ...], CFAD[{q1+ ..., {m^2, -1}}, ...], CFAD[q1,...] etc.

If s is not explicitly specified, 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 FeynCalcI internal form is performed by FeynCalcInternal, where a CFAD is encoded using the special head CartesianPropagatorDenominator.

See also

Overview, FAD, SFAD, GFAD, FeynAmpDenominator.

Examples

CFAD[{{p, 0}, m^2}]

1(p2+m2iη)\frac{1}{(p^2+m^2-i \eta )}

FeynAmpDenominatorExplicit[%]

1m2+p2\frac{1}{m^2+p^2}

CFAD[{{p, 0}, {m^2, 1}}]

1(p2+m2+iη)\frac{1}{(p^2+m^2+i \eta )}

FeynAmpDenominatorExplicit[%]

1m2+p2\frac{1}{m^2+p^2}

CFAD[{{p, 0}, -m^2}]

1(p2m2iη)\frac{1}{(p^2-m^2-i \eta )}

FeynAmpDenominatorExplicit[%]

1p2m2\frac{1}{p^2-m^2}

CFAD[{{0, p . q}, m^2}]

1(pq+m2iη)\frac{1}{(p\cdot q+m^2-i \eta )}

FeynAmpDenominatorExplicit[%]

1m2+pq\frac{1}{m^2+p\cdot q}

CFAD[{{0, p . q}}]

1(pqiη)\frac{1}{(p\cdot q-i \eta )}

FeynAmpDenominatorExplicit[%]

1pq\frac{1}{p\cdot q}