Quantum Field Theory Description of Processes Passing at Finite Space and Time Intervals

Abstract

We consider a new approach to the quantum field theory description of processes passing at finite space-time intervals. The formalism is based on the Feynman diagram technique in the coordinate representation supplemented with modified rules for the transition to the momentum representation reflecting specific experimental situations. This effectively implies that only the particle propagators in the momentum representation are modified, while the standard Feynman rules in the momentum representation remain unchanged. No wave packets are used in the approach, i.e., the initial and final states of particles are described by plane waves, which significantly simplifies the calculations. Three processes—neutrino oscillations, unstable particle decay, and neutral kaon oscillations—are used as examples to show that the proposed approach correctly reproduces the well-known results.