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

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.