Thermal fermionic dispersion relations in a magnetic field Original Research Article

The thermal self-energy of an electron in a static uniform magnetic field B is calculated to first order in the fine structure constant α and to all orders in eB. We use two methods, one based on the Furry picture and another based on Schwingerʹs proper-time method. As external states we consider relativistic Landau levels with special emphasis on the lowest Landau level. In the high-temperature limit we derive self-consistent dispersion relations for particle and hole excitations, showing the chiral asymmetry caused by the external field. For weak fields, earlier results on the ground-state energy and the anomalous magnetic moment are discussed and compared with the present analysis. In the strong-field limit the appearance of a field-independent imaginary part of the self-energy, related to Landau damping in the e+e− plasma, is pointed out.