  A convenient and general decomposition of the photon self-energy in a
magnetized, but otherwise isotropic, medium is given in terms of the minimal
set of tensors consistent with the transversality condition. As we show, the
self-energy in such a medium is completely parametrized in terms of nine
independent form factors, and they reduce to three in the long wavelength
limit. We consider in detail an electron gas with a background magnetic field,
and using finite temperature field theory methods, we obtain the one-loop
formulas for the form factors, which are exact to all orders in the magnetic
field. Explicit results are derived for a variety of physical conditions. In
the appropriate limits, we recover the well-known semi-classical results for
the photon dispersion relations and the Faraday effect. In more general cases,
where the semi-classical treatment or the linear approximation (weak field
limit) are not applicable, our formulas provide a consistent and systematic way
for computing the self-energy form factors and, from them, the photon
dispersion relations.
