Boost operator approach to the relativistic polarized SZ effect

Abstract: We extend the recent boost operator formalism for relativistic Compton scattering calculations to also account for polarization. This allows us to provide general, exact expressions for the polarized Sunyaev-Zeldovich (SZ) effect sourced both kinematically and from intrinsic anisotropies of the Cosmic Microwave Background (CMB). The results are given in terms of rational operator functions that can be used to generate distortion spectra that describe the general SZ signal, reproducing the classical polarized SZ results in the appropriate limits. Our derivation allows for clear separation of physical effects in the generation of polarized SZ, and beyond the SZ application provides a general description of the Compton collision term in the Doppler-dominated regime. Through direct computation of important example cases we further illustrate the power of this new method.