Lorentz group theory and polarization of the light

TL;DR

This paper explores the application of Lorentz group theory to light polarization, highlighting differences between isotropic and time-like vectors and revealing topological distinctions relevant to polarization optics and space-time structure.

Contribution

It connects Lorentz group properties with polarization optics, emphasizing the role of spinor formalism and topological differences in describing polarized light.

Findings

Differences between isotropic and time-like vectors affect polarization descriptions.

Spinor techniques reveal subtle topological distinctions in polarization.

Topological differences relate to the spinor structure of space-time.

Abstract

Some facts of the theory of the Lorentz group are specified for looking at the problems of light polarization optics in the frames of vector Stokes-Mueller and spinor Jones formalism. In view of great differences between properties of isotropic and time-like vectors in Special Relativity we should expect principal differences in describing completely polarized and partly polarized light. In particular, substantial differences are revealed when turning to spinor techniques in the context of the polarized light. Because Jones complex formalism has close relation to spinor objects of the Lorentz group, within the field of the light polarization we could have physical realizations on the optical desk of some subtle topological distinctions between orthogonal L_{+}^{\uparrow} =SO_{0}(3.1) and spinor SL(2.C) groups. These topological differences of the groups find their corollaries in the problem of the so-called spinor structure of physical space-time, some new points are considered.