THERMAL FERMIONIC DISPERSION-RELATIONS IN A MAGNETIC-FIELD

The thermal self-energy of an electron in a static uniform magnetic fi eld B is calculated to first order in the fine structure constant alph a and to all orders in eB. We use two methods, one based on the Furry picture and another based on Schwinger's proper-time method. As extern al states we consider relativistic Landau levels with special emphasis on the lowest Landau level. In the high-temperature limit we derive s elf-consistent dispersion relations for particle and hole excitations, showing the chiral asymmetry caused by the external field. For weak f ields, earlier results on the ground-state energy and the anomalous ma gnetic moment are discussed and compared with the present analysis. In the strong-field limit the appearance of a field-independent imaginar y part of the self-energy, related to Landau damping in the e(+)e(-) p lasma, is pointed out.