Description of processes passing at finite space and time intervals in the framework of QFT

Vadim Egorov,Igor Volobuev,D Melikhov,I Volobuev

doi:10.1051/epjconf/201922201009

Vadim Egorov, Igor Volobuev + Show 2 more

Open Access

https://doi.org/10.1051/epjconf/201922201009

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Abstract

We consider a new approach to the description in the framework of QFT of processes passing at finite space and time intervals. The formalism is based on the Feynman diagram technique in the coordinate representation, in which the rules of passing to the momentum representation are modified in accordance with the experimental setup of neutrino oscillation experiments. In effect, only the propagators of particles in the momentum representation are modified, while all the other standard Feynman rules in the momentum representation remain the same. Since the initial and final particle states are described by plane waves, the approach does not need the use of wave packets, which greatly simplifies the calculations of amplitudes. Taking as examples the processes of displaced pion decay, neutral kaon and neutrino oscillations we show that the approach under consideration correctly reproduces the known standard results.

Highlights

The standard perturbative S-matrix formalism and Feynman diagram technique allow one to describe a huge number of various processes of elementary particle interactions, and the results of the theoretical description are in an excellent agreement with the experimental data in the vast majority of cases
The use of the states with a definite strangeness or lepton flavor for describing the neutrino interactions and decays of neutral kaons leads to the well-known formulas for oscillations of neutrinos and neutral kaons, which are in a good agreement with the experimental data
A novel quantum field-theoretical approach to describing the processes passing at finite distances and finite time intervals is put forward

Summary

Introduction

The standard perturbative S-matrix formalism and Feynman diagram technique allow one to describe a huge number of various processes of elementary particle interactions, and the results of the theoretical description are in an excellent agreement with the experimental data in the vast majority of cases. There is a number of phenomena that cannot be described within the framework of the standard perturbation theory: these are, in particular, the phenomena of neutral meson and neutrino oscillations that occur at macroscopic space and time intervals For these phenomena one uses either a quantum mechanical description in terms of plane waves, or a field-theoretical description in terms of wave packet. In the present paper we show that the application of this approach to describing the processes of displaced unstable particle decay, neutral kaon and neutrino oscillations correctly reproduces the known results

Displaced pion decay

Neutral Kaon oscillations

Neutrino oscillations

Conclusion