  The perturbative calculation of the lifetime of charged excitations in
ultrarelativistic plasmas is plagued with infrared divergences which are not
eliminated by the screening corrections. The physical processes responsible for
these divergences are the collisions involving the exchange of longwavelength,
quasistatic, magnetic gluons (or photons), which are not screened by plasma
effects. In QED, the leading divergences can be resummed in a non-perturbative
treatement based on a generalization of the Bloch-Nordsieck model at finite
temperature. The resulting expression of the fermion propagator is free of
infrared problems, and exhibits a ``non-exponential'' damping at large times:
$S_R(t)\sim exp {-\alpha T t ln\omega_pt}$, where $\omega_p=eT/3$ is the plasma
frequency and $\alpha=e^2/4\pi$.
