Gauge independence and relativistic dispersion equations in statistical QED

The gauge parameter dependence of the particle spectra in statistical QED is revisited in a non-perturbative way and it is concluded that the electron spectra is gauge-parameter dependent, the physical spectra being obtained in the Landau gauge. We calculate in the one-loop approximation the gauge parameter dependent behavior of the electron dispersion equation at finite temperature and density, and consider the limit of T=0 and high density afterwards. The curves obtained confirm the predictions of the general results.