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We consider a novel approach to the quantum field-theoretical 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 passing 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. Two processes — a displaced decay of an unstable particle and neutrino oscillations — are used as examples to show that the proposed approach correctly reproduces the results of the standard quantum-mechanical description.