The Meaning of Coherence in Weak Decay Processes: `Neutrino Oscillations' Reconsidered

A Feynman path integral analysis of a two-neutrino-flavour electron appearence experiment following pion decay at rest recovers the standard oscillation phase, revealing an important contribution from the decay amplitude of the pion as well as an error in previous similar calculations by the present author. In the calculation, path amplitudes for different neutrino mass eigenstates add coherently, but no putative `neutrino flavour eigenstates' are invoked. It is shown that the coherent production of the latter states is incompatible with the measured values of $\Gamma(\pi \rightarrow {\rm e}\nu)/\Gamma(\pi \rightarrow \mu \nu)$ and the PMNS matrix elements. Application of the path integral approach to other two-path quantum interference experiments is compared with that to neutrino oscillations, and other treatments of the latter in the literature are discussed.