The Scaling Group of the Radiative Transfer Equation

We show that the equation of radiative transfer is invariant under a group of simultaneous transformations of the scale (i.e., the optical thickness) and the phase function. In this way, we provide a unified explanation of various empirical scaling laws, similarity relations and other approximations (especially delta-function approximations) which have been proposed in the literature. Connections with critical-point behavior in statistical mechanics are also indicated.