  Using the general form of the static energy solutions to the Dirac equation
with a magnetic field, we calculate a general self-energy matrix in the
Furry-picture. In the limit of high temperatures, but even higher magnetic
fields, a self-consistent dispersion relation is solved. In contrast to the
high temperature limit, this merely results in a small mass shift. The electron
anomalous magnetic moment is calculated. The contribution from thermal fermions
is found to be different from the corresponding contribution using perturbation
theory and plane-wave external states. In the low temperature limit the
self-energy is shown to exhibit de Haas--van Alphen oscillations. In the limit
of low temperatures and high densities, the self-energy becomes very large.
