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arXiv:2406.10799 · International Journal of Modern Physics A

Toward a quantum field theoretical description of oscillation effects

Maxim V Libanov

Published Aug 16, 2024• 2 citations
arXivHTMLPDF

Abstract

In this paper, we propose an approach based on the theory of an axiomatic S matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field theory. We discuss the relation of the proposed approach with other approaches based on considering of wave packets as asymptotic states or introducing of “distance- or time-dependent propagators”.

DOI
10.1142/s0217751x24450027

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In this paper, we propose an approach based on the theory of an axiomatic S matrix and partially switching on an interaction, which is extremely suitable for describing the phenomenon of oscillations within the framework of quantum field theory. We discuss the relation of the proposed approach with other approaches based on considering of wave packets as asymptotic states or introducing of “distance- or time-dependent propagators”.
The interaction of a quantum system with an oscillating field is studied in a formalism which replaces the semiclassical time-dependent Hamiltonian with a time-independent Hamiltonian represented by an infinite matrix. The formalism is developed as a mathematical equivalent to the semiclassical treatment, and interpreted as a classical approximation to the quantum treatment of the field. Combined with a perturbation theory for two nearly degenerate states, the formalism provides a convenient method for determining resonance transition probabilities including frequency shifts and multiple quantum transitions. The theory is illustrated by a detailed study of the simple case of a two-state system excited by a strong oscillating field.
We consider a class of models for the relativistic covariant wave packets (WPs) which can be used as asymptotically free in and out states in the quantum field theoretical formalisms for description of the neutrino flavor oscillation phenomenon. We demonstrate that the new “asymmetric” wave packet (AWP) is an appropriate alternative to the more conventional “symmetric” WPs, like the so-called relativistic Gaussian packet (RGP) widely used in the quantum field theory (QFT)-based approaches to neutrino oscillations. We show that RGP is not a particular case of AWP, although many properties of these models are almost identical in the quasistable regime. We discuss some features of AWP distinguishing it from RGP.
In a quantum field approach to neutrino oscillations, the neutrino is treated as a propagator, while the external initial and final particle states are described by covariant wave packets. For the asymptotic behavior on short and long macroscopic baselines, the wave packet modified neutrino propagator is expressed through asymptotic series in powers of dimensionless Lorentz and rotation invariant variables. In both regimes, leading-order corrections violate the classical inverse-square law and lead to a decrease in the neutrino-induced event rate. The possibility that the so-called reactor antineutrino anomaly can, at least partially, be explained within this approach is discussed.
With the use of a quantum theory of optical propagation, a set of nonlinear stochastic partial differential equations may be derived which describes the quantum-statistical properties of traveling waves due to self-phase modulation in a nonlinear medium. We calculate exact moments for the field, which exhibit classical self-phase modulation in the short-interaction limit and periodic quantum evolution through field-superposition states in the long-interaction limit. Reversible and irreversible behaviors of the stochastic description are reviewed. The relation of the present work to the corresponding single-mode nonlinear oscillator is discussed.
The paper proposes a model of a unitary quantum field theory where the particle is represented as a wave packet.The frequency dispersion equation is chosen so that the packet periodically appears and disappears without changing its form.The envelope of the process is identified with a conventional wave function.Equation of such a field is nonlinear and relativistically invariant.With proper adjustments, they are reduced to Dirac, Schroedinger and Hamilton-Jacobi equations.A number of new experimental effects are predicted both for high and low energies.