Emergence of new quasiparticles in quantum electrodynamics at finite temperature

We study the spectrum of fermionic excitations in a hot relativistic electron plasma. Numerical analysis of the one-loop electron propagator shows the appearance of new quasiparticle modes, as already studied in the massless fermion limit, as the temperature is raised to exceed the electron mass $m$. We calculate the relevant spectral densities and show that one mode, whose splitting in energy from the original electron is of the order of $m$, moves as the temperature is raised towards higher frequency along with the electron while retaining a narrow width. We compare results derived in Feynman and Coulomb gauges. The role of the zero-temperature counterterms is discussed.