Ausl. J. Phys., 1983,36, 755-74 Dirac's equation in the presence of a static magnetic field is solved in terms of both cartesian and cylindrical coordinates, and solutions are found for three different spin operators. Choosing the spin to correspond to the parallel component Ilz of the magnetic moment operator leads to wavefunctions (a) which are symmetric between electron and positron states and (b) which are eigenfunctions of the Hamiltonian including radiative corrections. A vertex function [y:',~(k)l~ is defined and shown to be proportional to a gauge independent quantity [T::~(k)l". Symmetry properties of [T~:~(k)l~ are derived in the case where the spin corresponds to Ilz. The use of the vertex function is illustrated by deriving the electron propagator in coordinate space from the vacuum expectation value. Properties of functions J~, _n(x) which appear extensively and are related to generalized Laguerre polynomials are derived and summarized in the Appendix.

Aust. J. Phys., 1983, 36, 799-824 A version of QED is developed which allows one to treat electron-photon interactions in the magnetized vacuum exactly and which allows one to calculate the responses of a relativistic quantum electron gas and include these responses in QED. Gyromagnetic emission and related crossed processes, and Compton scattering and related processes are discussed in some detail. Existing results are corrected or generalized for nonrelativistic (quantum) gyroemission, one-photon pair creation, Compton scattering by electrons in the ground state and two-photon excitation to the first Landau level from the ground state. We also comment on maser action in one-photon pair annihilation.

Aust. J. Phys., 1987,40, 1-21 The electron self-energy in a magnetic field is calculated with the effect of the field included exactly. A new representation of the wavefunctions and other quantities is defined, in which the mass operator has a particularly simple form. After renormalisation, the form of the mass operator allows corrections to the Dirac equation, wavefunctions, vertex function and the electron propagator close to the mass shell to be calculated to lowest order in the fine structure constant. The probability for an electron to change spin while remaining in the same Landau level is calculated, and is found to be much less than the probability of cyclotron emission.

Techniques in QED (quantum electrodynamics) have been developed previously (see for example Melrose and Parle 1983) allowing one to treat electron-photon and photon-photon interactions exactly in the magnetized vacuum and allowing one to include the effects of a medium. These techniques are extended to include particle-particle interactions. Exact cross-sections for electron-electron collisions are derived and compared with known expressions. Such calculations have application in studies of the formation and transfer of radiation in the atmospheres surrounding neutron stars.

The cyclotron line in Her X-1 is a hard X-ray feature at ≈ 58 keV discovered by Trümper et al. (1977). A cyclotron emission line at about this energy had been predicted by Gnedin and Sunyaev (1974) and Basko and Sunyaev (1975). They developed a model for the infall of accreted matter onto a magnetized neutron star’s surface, and concluded that hot spots would form at the polar caps and radiate X-rays. They predicted that the optional depth for bremsstrahlung would be less than unity, that for Compton scattering greater than unity and that for cyclotron absorption much greater than unity. A cyclotron line is then implied due to the emission spectrum lying below the black-body spectrum except near the cyclotron energy where it rises up to the black-body limit. More recent developments of these background ideas have been reviewed by Börner (1980).