Description of processes passing at finite space-time intervals in the framework of quantum field theory

Abstract

We consider a novel quantum field-theoretical approach to the description of processes passing at finite space-time intervals based on the Feynman diagram technique in the coordinate representation. The most know phenomena of this type are neutrino and neutral kaon oscillations. The experimental setting of these processes demands that the rules of passing to the momentum representation in the Feynman diagram technique be adjusted in accordance with it, which leads to a modification of the Feynman propagator in the momentum representation. The approach does not make use of wave packets: both initial and final particle states are described by plane waves, which simplifies the calculations considerably. We demonstrate the validity of the formalism by applying it to describing the decay of an unstable particle and neutrino oscillations. It is shown that the considered approach correctly reproduces the known results.