  The calculation of the lifetime of quasiparticles in a QED plasma at high
temperature remains plagued with infrared divergences, even after one has taken
into account the screening corrections. The physical processes responsible for
these divergences are the collisions involving the exchange of very soft,
unscreened, magnetic photons, whose contribution is enhanced by the thermal
Bose-Einstein occupation factor. The self energy diagrams which diverge in
perturbation theory contain no internal fermion loops, but an arbitrary number
of internal magnetostatic photon lines. By generalizing the Bloch-Nordsieck
model at finite temperature, we can resum all the singular contributions of
such diagrams, and obtain the correct long time behaviour of the retarded
fermion propagator in the hot QED plasma: $S_R(t)\sim \exp\{-\alpha T \, t\,
\ln\omega_pt\}$, where $\omega_p=eT/3$ is the plasma frequency and
$\alpha=e^2/4\pi$.
