2012/11/24 by Е. М. Ovsiyuk, E. M. Ovsiyuk, О. В. Веко +11
Engineering · Materials Science · Mathematics · Physics and Astronomy · #35 #FOS: Physical sciences #G.1 #Liquid Crystal Research Advancements #Mathematical Physics (math-ph) #Optical Polarization and Ellipsometry #Optics (physics.optics) #Photorefractive and Nonlinear Optics #acm:35 #math-ph #math.MP #msc:35 #physics.optics
paper · pdf · doi:10.48550/arxiv.1211.5667
15 pages. Report to The International Conference "Differential Geometry and Dynamical Systems - 2012". 29 August - 2 September 2012, Mangalia, Romania
arxiv created 2012/11/24 · openalex publication_date 2012/11/24 · arxiv updated 2012/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the context of applying the Lorentz group theory to polarization optics in the frames of Stokes-Mueller formalism, some properties of the Lorentz group are investigated. We start with the factorized form of arbitrary Lorentz matrix as a product of two commuting and conjugate 4× 4-matrices, L(q,q)= A(qa) A^*(qa); a= 0,1,2,3. Mueller matrices of the Lorentzian type M=L are pointed out as a special sub-class i n the total set of 4× 4 matrices of the linear group GL(4,R). Any arbitrary Lorentz matrix is presented as a linear combination of 16 elements of the Dirac basis. On this ground, a method to construct parameters qa by an explicitly given Lorentz matrix L is elaborated. It is shown that the factorized form of L=M matrices provides us with a number of simple transitivity equations relating couples of initial and final 4-vectors, which are defined in terms of parameters qa of the Lorentz group. Some of these transitivity relations can be interpreted within polarization optics and can be applied to the group-theoretic analysis of the problem of measuring Mueller matrices in optical experiments.