Transitivity in the theory of the Lorentz group and the Stokes -- Mueller formalism in optics

Abstract

Group-theoretical analysis of arbitrary polarization devices is performed, based on the theory of the Lorentz group. In effective "non-relativistic" Mueller case, described by 3-dimensional orthogonal matrices, results of the one polarization measurement determine group theoretical parameters within the accuracy of an arbitrary numerical variable. There are derived formulas, defining Muller parameter of the non-relativistic Mueller device uniquely and in explicit form by by the results of two independent polarization measurements. Analysis is extended to Lorentzian optical devices, described by 4-dimensional Mueller matrices.