Analytical solution of the radiative transfer equation for polarized light

TL;DR

This paper introduces a novel formalism for polarized light transfer, representing Stokes parameters as four-vectors in a Minkowski-like space, and solves the radiative transfer equation using group theory methods.

Contribution

It presents a new formalism where the radiative transfer equation is an infinitesimal transformation under the Poincare group, offering a group-theoretic solution approach.

Findings

Stokes parameters form four-vectors in Minkowski-like space

The radiative transfer equation is an infinitesimal Poincare transformation

A finite element solution to the transfer equation is proposed

Abstract

A new formalism is introduced for the transfer of polarized radiation. Stokes parameters are shown to be four-vectors in a Minkowski-like space and, most strikingly, the radiative transfer equation (RTE) turns out to be an infinitesimal transformation under the Poincare (plus dilatations) group. A solution to the transfer equation as a finite element of this group is proposed.