Elementary constituents of the group SL(4,R), and classification of the Mueller matrices

Abstract

The goal of this paper is to develop a systematic method of locating the Mueller matrices within the class of the matrices of the real group SL(4, R). The main idea is to construct the general transformation of the group SL(4, R) (whose real matrices have unit determinant) is straightforward, but to analyze the adequacy of such a transformation for describing Mueller matrices is highly nontrivial. However, using the technique of Dirac matrices, we can quite easy and explicitly describe all the 16 one-parametric subgroups, from which, using the all possible products, emerges the whole group SL(4, R). As a matter of fact, for these separate 1-parametric subgroups the question of their adequacy of describing Mueller matrices becomes sufficiently simple and thus we obtain in each case a definite answer.