A tensor formalism for transfer and Compton scattering of polarized light

TL;DR

This paper introduces a new covariant tensor formalism for describing the transfer and Compton scattering of polarized light, enabling more flexible and relativistically consistent calculations, especially relevant for astrophysical phenomena like the Sunyaev-Zeldovich effect.

Contribution

It presents a novel tensor-based covariant formalism for polarized light transfer and scattering, extending traditional methods and facilitating relativistic calculations in astrophysics.

Findings

Developed a tensor formalism for polarized light

Derived a covariant kinetic equation for Compton scattering

Generalized the equation for arbitrary electron distributions

Abstract

A novel covariant formalism for the treatment of the transfer and Compton scattering of partially polarized light is presented. This was initially developed to aid in the computation of relativistic corrections to the polarization generated by the Sunyaev-Zeldovich effect (demonstrated in a companion paper), but it is of more general utility. In this approach, the polarization state of a light beam is described by a tensor constructed from the time average of quadratic products of the electric field components in a local observer frame. This leads naturally to a covariant description which is ideal for calculations involving the boosting of polarized light beams between Lorentz frames, and is more flexible than the traditional Stokes parameter approach in which a separate set of polarization basis vectors is required for each photon. The covariant kinetic equation for Compton scattering of partially polarized light by relativistic electrons is obtained in the tensor formalism by a heuristic semi-classical line of reasoning. The kinetic equation is derived first in the electron rest frame in the Thomson limit, and then is generalized to account for electron recoil and allow for scattering from an arbitrary distribution of electrons.