Lifetime of Quasiparticles in Hot QED Plasmas

The calculation of the lifetime of quasiparticles in a QED plasma at high temperature remains plagued with infrared divergences, even after including the screening corrections. We argue that the self-energy diagrams which give the dominant divergences contain no internal fermion loops, but an arbitrary number of magnetostatic photon lines. A generalization of the Bloch-Nordsieck approximation allows us to resum all the singular contributions of such diagrams, and to obtain the correct long time behavior of the retarded fermion propagator: $S_R\left(t\right)\sim \exp \{-\alpha \mathrm{Tt}\ln {\omega }_{p}t\}$, where ${\omega }_p=eT/3\mathrm{}$ is the plasma frequency and $\alpha {=e}^2/4\mathrm{}\pi$.