  Here we discuss the description of flavor neutrinos produced or detected in
processes which involve more than one neutrino. We show that in these cases
flavor neutrinos cannot be separately described by pure states, but require a
density matrix description. We consider explicitly the examples of $\nu_{e}$
and $\bar\nu_{\mu}$ production in $\mu^{+}$ decay and $\nu_{\mu}$ detection
through scattering on electrons. We show that the density matrix which
describes a flavor neutrino can be approximated with a density matrix of a pure
state only when the differences of the neutrino masses are neglected in the
interaction process. In this approximation, the pure states are the standard
flavor states and one recovers the standard expression for the neutrino
oscillation probability. We discuss also the effects of mixing of the three
standard light neutrinos with heavy neutrinos which can be either decoupled
because their masses are much larger than the maximum neutrino energy in the
neutrino production process or because they are produced and detected
incoherently. Finally, we discuss the more complicated case of
neutrino-electron elastic scattering, in which the initial and final neutrinos
do not have determined flavors, but there is a flavor dependence due to the
different contributions of charged-current and neutral-current interactions.
