FeynCalc manual (development version)

FCLoopMixedToCartesianAndTemporal

FCLoopMixedToCartesianAndTemporal[int, {q1, q2, ...}] attempts to convert loop integrals that contain both Lorentz and Cartesian or temporal indices/momenta to pure temporal and Cartesian indices.

See also

Overview

Examples

FCI@SFAD[q] 
 
FCLoopMixedToCartesianAndTemporal[%, {q}, FCE -> True]

1(q2+iη)\frac{1}{(q^2+i \eta )}

1(q2(q0)2iη)-\frac{1}{(q^2-\left(q^0\right)^2-i \eta )}

FCI@SFAD[{q1 + q2 + p, m^2}] 
 
FCLoopMixedToCartesianAndTemporal[%, {q1, q2}]

1((p+q1+q2)2m2+iη)\frac{1}{((p+\text{q1}+\text{q2})^2-m^2+i \eta )}

1((p+q1+q2)2+m2((p+q1+q2)0)2iη)-\frac{1}{((p+\text{q1}+\text{q2})^2+m^2-\left((p+\text{q1}+\text{q2})^0\right)^2-i \eta )}

FCI[TC[k] FVD[k, mu] FAD[k, k + p]] 
 
FCLoopMixedToCartesianAndTemporal[%, {k}]

k0kmuk2.(k+p)2\frac{k^0 k^{\text{mu}}}{k^2.(k+p)^2}

k0(k0gˉ0muk$g$mu)(k2(k0)2iη).((k+p)2((k+p)0)2iη)\frac{k^0 \left(k^0 \bar{g}^{0\text{mu}}-k^{\$} g^{\$\text{mu}}\right)}{(k^2-\left(k^0\right)^2-i \eta ).((k+p)^2-\left((k+p)^0\right)^2-i \eta )}