Quantum Field Theory Beyond the S-Matrix Formalism
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antum Field Theory Beyond the S-Matrix Formalism I. P. Volobueva, * and V. O. Egorova, b aSkobel’tsyn b
Institute of Nuclear Physics, Moscow State University, Moscow, 119991 Russia Faculty of Physics, Moscow State University, Moscow, 119991 Russia *e-mail: [email protected]
Received December 20, 2019; revised January 16, 2020; accepted January 29, 2020
Abstract—Particle transitions passing over finite space and time intervals are self-consistently described within a novel quantum field-theoretical approach based on Feynman diagrams in configuration space. The transition to momentum space is performed following the rules modified so as to consider the geometry of neutral-meson and neutrino oscillation experiments. Using the processes of decay of an unstable scalar particle at a macroscopic distance from the source and of neutral kaon and neutrino oscillations as examples, we demonstrate that their known characteristics are adequately reproduced within the proposed approach. DOI: 10.1134/S1063779620040760
1. INTRODUCTION Quantum field theory in its present form is actually reduced to the perturbative S-matrix formalism within the Standard Model or its extensions. Thereby, a precise description of a great number of processes of particle interactions is obtained in the framework of the Standard Model and, as a rule, the theory is well corroborated by the experimental data. Still, a number of physical phenomena cannot be described in terms of the standard S-matrix perturbation theory. These include neutral meson and neutrino oscillations, which proceed over finite space and time intervals. Thus, the well-known and experimentally studied process of neutrino oscillation is usually viewed as a transition from one neutrino flavor eigenstate, i.e. a state with a definite flavor but no definite mass, into another neutrino flavor eigenstate depending on the distance traveled [1, 2]. However, the standard theoretical description of this phenomenon should be viewed as eclectic since the production of neutrino flavor eigenstates is described within quantum field theory, and their time evolution within quantum mechanics, which actually is an integral part of the former. Apart from that, the broadly accepted standard description of neutrino oscillation relies on the plane-wave approximation whereby conservation of energy and momentum is violated for the process of flavor-eigenstate production. The latter problem can presumably be circumvented by assuming realistic wave packets rather than plane waves, but this renders the calculation of transition amplitudes rather cumbersome. The problems arising in the standard treatment of neutrino oscillations are extensively discussed in the literature [3–5].
An alternative S-matrix approach to describing the neutrino oscillation processes was proposed in [3]. In the latter, neutrino is produced as an off-shell particle and its propagation is described by the Feynman propagator, so that energy and momentum are automatically conserved. In this approach, neutrino oscillation is trea
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