Some New Results in the Group-theoretical Description of the Radiation Transfer

Abstract

The paper presents some new results of investigation developing the approach aimed at applying the group theory methods to radiation transfer problems. It consists of two separate parts. In the first part we derive new properties of supersymmetry of fundamental supermatrices - representations of composition and translation groups. It is shown that these supermatrices, which determine the layers adding to the two opposite boundaries of inhomogeneous medium, are connected with each other by the procedure of parity transposition. It is also demonstrated that, by analogy with the common second order matrices, the considered supermatrices can be factorized yielding the product of triangular supermatrices. The second part generalizes and applies the concept of composition groups to the case of media with spherical symmetry.