Groups and their Representations in the Theory of Radiative Transfer. III.

This is the last of a series of papers devoted to the application of group theoretical methods for astrophysical radiative transfer problems. The superdeterminant of the supermatrix-operators of the composition and translation groups for inhomogeneous absorbing and scattering media of finite thickness is proved to equal unity. The feasibility of applying a group approach for determining the statistical average quantities describing radiative diffusion is demonstrated. A variational principle is used for the diffusion of radiation in homogeneous media, a formulation of Hamilton's principle is given, and the corresponding Lagrangians and conservation law are found. Examples are given of two parameter composition groups introduced for nonstationary radiative transfer problems and problems involving the diffusion of radiation in turbulent media. [ABSTRACT FROM AUTHOR]