  We present a theoretical study of radiative transfer in strongly magnetized
electron-ion plasmas, focusing on the effect of vacuum polarization due to
quantum electrodynamics. This study is directly relevant to thermal radiation
from the surfaces of highly magnetized neutron stars, which have been detected
in recent years. Strong-field vacuum polarization modifies the photon
propagation modes in the plasma, and induces a ``vacuum resonance'' at which a
polarized X-ray photon propagating outward in the neutron star atmosphere can
convert from a low-opacity mode to a high-opacity mode and vice versa. The
effectiveness of this mode conversion depends on the photon energy and the
atmosphere density gradient. For a wide range of field strengths, $7\times
10^{13}< B < 10^{16}$ G, the vacuum resonance lies between the photospheres of
the two photon modes, and the emergent radiation spectrum from the neutron star
is significantly modified by the vacuum resonance. (For lower field strengths,
only the polarization spectrum is affected.) Under certain conditions, which
depend on the field strength, photon energy and propagation direction, the
vacuum resonance is accompanied by the phenomenon of mode collapse (at which
the two photon modes become degenerate) and the breakdown of Faraday
depolarization. Thus, the widely used description of radiative transfer based
on photon modes is not adequate to treat the vacuum polarization effect
rigorously. We study the evolution of polarized X-rays across the vacuum
resonance and derive the transfer equation for the photon intensity matrix
(Stokes parameters), taking into account the effect of birefringence of the
plasma-vacuum medium, free-free absorption, and scatterings by electrons and
ions.
