Relativistic effects on the photon propagation in a strongly magnetized plasma

The propagation of photons in an electron plasma in the presence of a uniform magnetic field is treated on a fully quantum mechanical, relativistic basis. The general expression for the complex refractive index of the two polarisation modes is derived within second-order S-matrix theory. For physical conditions associated with X-ray pulsars, results are presented for both the real and the imaginary part of the refractive index as a function of frequency for different temperatures and angles of propagation. Comparing with previous non-relativistic calculations, the authors find decisive modifications in the vicinity of the resonances, which are essentially caused by the different structure of the relativistic laws of conservation.