Lifetimes of quasiparticles and collective excitations in hot QED plasmas

Abstract

The perturbative calculation of the lifetime of fermion excitations in a QED plasma at high temperature 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 long wavelength, quasistatic, magnetic photons, which are not screened by plasma effects. The leading divergences can be resummed in a nonperturbative treatment based on a generalization of the Bloch-Nordsieck ͑BN͒ model at finite temperature. The resulting expression of the fermion propagator is free of infrared problems, and exhibits a nonexponential damping at large times: S R (t)ϳexp͕Ϫ␣Tt ln p t͖, where p ϭeT/3 is the plasma frequency and ␣ϭe 2 /4. ͓S0556-2821͑97͒00802-3͔

The quark–gluon plasma: collective dynamics and hard thermal loops

“…We conclude this subsection with two comments: First, we notice that the previous analysis has been extended to massive test particles [98], and also to soft quasiparticles, that is, to collective fermionic excitations with typical momenta p ∼ eT [97]. It has also been shown that the result presented here is gauge invariant [98].…”

“…We refer to this class of diagrams as to the "quenched approximation" (no fermion loops are included except for the hard thermal loops dressing the soft photons lines). One can verify [68,97] leading infrared contribution to γ p comes from these diagrams where the internal fermion lines are hard and nearly on-shell. The individual contributions of these diagrams to the damping rate contain power-like infrared divergences.…”

“…[97,98], this second order correction to the retarded propagator exponentiates in an all-order calculation:…”

“…[97,98] these antiperiodic boundary conditions, which greatly complicate the solution of the BN equation, are not needed to obtain the dominant behaviour at large time of the fermion propagator: this is indeed identical to that of a test particle, by which we mean a particle which is distinguishable from the plasma particles, and is therefore not part of the thermal bath. The propagator of a test particle has only one analytic component, namely S > (S < vanishes since the thermal bath acts like the vacuum for the field operators of the test particle).…”

“…A more complicated behaviour can occur whenever some of the aforementioned assumptions are not satisfied. In section 6, we shall encounter an example of such a non-trivial evolution in time [68,97,98,99].…”