Calculation of Feynman diagrams in space and time by stationary phase

Feynman diagrams are usually derived in relativistic space and time, and then immediately converted into energy and momentum by a Fourier transform. A method is proposed that allows keeping the external vertices at fixed locations and finite times, while the internal vertices are integrated in space-time as well. Propagators between the vertices are the well-known Bessel functions of the relativistic distance. The example of the Compton effect is worked out.