A classification of electron and optical polarization transfer matrices

Abstract

In the Stokes parameter formulation of electron and optical polarization, interactions which alter the state of beam polarization are represented by 4*4 transfer matrices. A classification scheme has been introduced for these matrices based on criteria descriptive of their behaviour under unitary similarity transformations. It is shown in particular that nonsingular transfer matrices may be organized in a group which is homomorphic on the Lorentz group and this result allows the polarizing action of a number of dissimilar processes to be described in terms of a simple geometrical picture. The results have been illustrated by a number of examples selected from the field of optics and two forms of electron scattering, which provide the bases of methods for producing polarized electrons, have been analysed in detail.