  The production and decay rate of massive sterile neutrinos at finite
temperature receives next-to-leading order corrections from the gauge
interactions of lepton and Higgs doublets. Using the Closed-Time-Path approach,
we demonstrate that the perturbatively obtained inclusive rate is finite. For
this purpose, we show that soft, collinear and Bose divergences cancel when
adding the tree-level rates from 1<->3 and 2<->2 processes to vertex and
wave-function corrections to 1<->2 processes. These results hold for a general
momentum of the sterile neutrino with respect to the plasma frame. Moreover,
they do not rely on non-relativistic approximations, such that the full
quantum-statistical effects are accounted for to the given order in
perturbation theory. While the neutrino production rate is of relevance for
Leptogenesis, the proposed methods may as well be suitable for application to a
more general class of relativistic transport phenomena.
