DOES IT POSSIBLE FINSLER GEOMETRIZATION OF THE POLARIZATION OPTICS?
2012jkq | Ovsiyuk E.M., Redkov V.M.  // Mozyr State Pedagogical University, Mozyr, Belarus; Institute of Physics, National Academy of Sciences of Belarus, Minsk, Belarus, e.ovsiyuk@mail.ru, v.redkov@dragon.bas-net.by

This paper provides an overview of some of the features of the matrix calculus to analyze the issues of polarization optics. There is reason to believe that methods of Finsler geometry can be of help here. Since the Mueller matrices, acting on real four-dimensional Stokes vectors, are real, then in possible studies of Mueller matrices one can use their parametrization obtained by applying the Dirac basis. The law of multiplication for the elements of the original group is complicated, but it is suitable for analytical study. The explicit form of the determinant of any matrix in this parametrization, provides us with a natural classifying invariant in a variety of the matrices. This parametrization is used to describe the possible classes of Mueller matrices, including the degenerate cases of matrices with zero determinant, described within the structure of semigroups. It turns out that imposing linear relationships on the 16 parameters that are compatible with the group multiplication law, we can specify mostly classes of degenerate matrices with the structure of semigroups. A complete classification of such semigroups of rank 1, 2, 3 is elaborated.

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