We perform a detailed analysis of the damping rate of a moving fermion in hot QED. Using bare propagators and taking a slightly off-shell fermion, we prove the cancellation of both magnetic and electric infrared singularities at two-loop order. Although infrared finite, the perturbation series is very badly behaved when the fermion is taken on shell. This problem is overcome by resumming both the hard loops in the photon propagator and the damping rate in the fermion propagator. The damping rate can only be calculated through a Schwinger-Dyson equation. We also study the gauge independence of our result.

Using thermal field theory methods, we recalculate axion emission from dense plasmas. We study in particular the Primakoff and the bremsstrahlung processes. The Primakoff rate is significantly suppressed at high densities, when the electrons become relativistic. However, the bound on the axion-photon coupling, G < 10 −10 GeV, is unaffected, as it is constrained by the evolution of HB stars, which have low densities. In contradistinction, the same relativistic effects enhance the bremsstrahlung processes. From the red giants and white dwarfs evolution, we obtain a conservative bound on the axion-electron coupling, g ae < 2 × 10 −13 .

We report various many-body theoretical approaches to the nonlinear decay rate and energy loss of charged particles moving in an interacting free electron gas. These include perturbative formulations of the scattering matrix, the self-energy, and the induced electron density. Explicit expressions for these quantities are obtained, with inclusion of exchange and correlation effects.

Using thermal field theory, we derive simple analytic expressions for the spectral density of photons in degenerate QED plasmas, without assuming the usual non or ultra-relativistic limit. We recover the standard results in both cases. Although very similar in ultra-relativistic plasmas, transverse and longitudinal excitations behave very differently as the electron Fermi momentum decreases.