Kinetic theory of polarization in the Sunyaev-Zeldovich effect

We apply the coherency tensor formalism to the calculation of the spectral distortions imprinted in the intensity and polarization of the cosmic microwave background radiation due to the kinematic and thermal Sunyaev-Zeldovich effects (SZE). We obtain the first relativistic corrections to the intensity produced by the kinematic and thermal SZE, and the first correction to the polarization magnitude due to electron thermal motion.