  We consider several subtle aspects of the theory of neutrino oscillations
which have been under discussion recently. We show that the $S$-matrix
formalism of quantum field theory can adequately describe neutrino oscillations
if correct physics conditions are imposed. This includes space-time
localization of the neutrino production and detection processes. Space-time
diagrams are introduced, which characterize this localization and illustrate
the coherence issues of neutrino oscillations. We discuss two approaches to
calculations of the transition amplitudes, which allow different physics
interpretations: (i) using configuration-space wave packets for the involved
particles, which leads to approximate conservation laws for their mean energies
and momenta; (ii) calculating first a plane-wave amplitude of the process,
which exhibits exact energy-momentum conservation, and then convoluting it with
the momentum-space wave packets of the involved particles. We show that these
two approaches are equivalent. Kinematic entanglement (which is invoked to
ensure exact energy-momentum conservation in neutrino oscillations) and
subsequent disentanglement of the neutrinos and recoiling states are in fact
irrelevant when the wave packets are considered. We demonstrate that the
contribution of the recoil particle to the oscillation phase is negligible
provided that the coherence conditions for neutrino production and detection
are satisfied. Unlike in the previous situation, the phases of both neutrinos
from $Z^0$ decay are important, leading to a realization of the
Einstein-Podolsky-Rosen paradox.
