Calculation of Feynman diagrams in space and time by stationary phase

Abstract

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.