Relativistic kinetic equation for Compton scattering of polarized radiation in strong magnetic field

We derive the relativistic kinetic equation for Compton scattering of polarized radiation in strong magnetic field using the Bogolyubov method. The induced scattering and the Pauli exclusion principle are taken into account. The electron polarization is also considered in the general form of the kinetic equation. The special forms of the equation for the cases of the non-polarized electrons, the rarefied electron gas and the two polarization mode description of radiation are found. The derived equations are valid for any photon and electron energies and the magnetic field strength below about 10^{16} G. These equations provide the basis for formulation of the equation for polarized radiation transport in atmospheres and magnetospheres of strongly magnetized neutron stars.Comment: 23 pages, accepted for publication in Phys. Rev.