We study several aspects of the kinetic approach to sterile neutrino
production via active-sterile mixing. We obtain the neutrino propagator in the
medium including self-energy corrections up to O(GF2β), from which
we extract the dispersion relations and damping rates of the propagating modes.
The dispersion relations are the usual ones in terms of the index of refraction
in the medium, and the damping rates are Ξ1β(k)=Ξaaβ(k)cos2ΞΈmβ(k);Ξ2β(k)=Ξaaβ(k)sin2ΞΈmβ(k) where
Ξaaβ(k)βGF2βkT4 is the active neutrino scattering rate and
ΞΈmβ(k) is the mixing angle in the medium. We provide a generalization of
the transition probability in the \emph{medium from expectation values in the
density matrix}: Paβsβ(t)=4sin22ΞΈmββ[eβΞ1βt+eβΞ2βtβ2eβ1/2(Ξ1β+Ξ2β)tcos(ΞEt)] and
study the conditions for its quantum Zeno suppression directly in real time. We
find the general conditions for quantum Zeno suppression, which for msββΌkeV sterile neutrinos with sin2ΞΈβ²10β3 \emph{may
only be} fulfilled near an MSW resonance. We discuss the implications for
sterile neutrino production and argue that in the early Universe the wide
separation of relaxation scales far away from MSW resonances suggests the
breakdown of the current kinetic approach.Comment: version to appear in JHE