  The aim of this work is to solve the dispersion relations near the first
excitation threshold of photon propagating along the magnetic field in the
strong field limit. We have calculated the time damping of the photon in two
particular cases: the degenerate gas as well as the diluted gas limit being
both important from the Astrophysical point of view. In particular the diluted
gas limit could describe the magnethosphere of neutron stars. The solutions
have been used to obtain a finite Quantum Faraday angle in both limits. A
resonant behavior for the Faraday angle is also obtained. To reproduce the
semi-classical result for the Faraday rotation angle the weak field limit is
considered.
