The Description of Neutrino and Muon Oscillations by Interfering Amplitudes of Classical Space-Time Paths

TL;DR

This paper analyzes neutrino and muon oscillations using Feynman's path amplitude approach, revealing new contributions to the oscillation phase from the source particle's space-time propagator, and deriving formulas for various decay scenarios.

Contribution

It introduces a novel analysis of particle oscillations through path amplitudes, highlighting the source particle's propagator effect and providing new oscillation phase formulas.

Findings

Neutrino oscillation phases differ from conventional formulas.

Source particle's space-time propagator significantly affects oscillation phases.

Derived formulas for oscillations following various decay processes.

Abstract

Particle oscillations following neutrino production processes are analysed within Feynman's path amplitude formulation of quantum mechanics. Consideration of the temporal sequence of production and detection events reveals an important contribution to the oscillation phase from the space-time propagator of the decaying source particle. Formulae are derived for spatial neutrino oscillations following pion decay (at rest and in flight), muon decay and nuclear $\beta$-decay at rest, as well as for similar muon oscillations after pion decay at rest and in flight. In all cases studied, the neutrino oscillation phases found differ from the conventionally used one. A concise critical review is made of previous treatments of the quantum mechanics of neutrino and muon oscillations.