  This report deals with the quantum theory of flavor oscillations in vacuum,
extended to fermionic particles in the several subtle aspects of the first and
second quantization theories. In this scenario, the use of the Dirac equation
is required for a satisfactory evolution of fermionic mass-eigenstates since in
the standard treatment of oscillations the mass-eigenstates are implicitly
assumed to be scalars and, consequently, the spinorial form of neutrino wave
functions is not included in the calculations. Within first quantized theories,
besides flavor oscillations, chiral oscillations automatically appear when we
set the dynamic equations for a fermionic Dirac-type particle. The left-handed
chiral nature of created and detected neutrinos can be implemented in the first
quantized Dirac theory in presence of mixing; the probability loss due to the
changing of initially left-handed neutrinos to the undetected right-handed
neutrinos can be obtained in analytic form. In the context of a causal
relativistic theory of a free particle, one of the two effects should be
present in flavor oscillations: (a) rapid oscillations or (b) initial flavor
violation. Concerning second quantized approaches, a simple second quantized
treatment exhibits a tiny but inevitable initial flavor violation without the
possibility of rapid oscillations. Such effect is a consequence of an
intrinsically indefinite but approximately well defined neutrino flavor. The
violation effects are shown to be much larger than loop induced lepton flavor
violation processes, already present in the standard model in the presence of
massive neutrinos with mixing. The conclusions of this report lead to lessons
concerning flavor mixing, chiral oscillations, interference between positive
and negative frequency components of Dirac equation solutions, and the field
formulation of quantum oscillations.
