Systems without symmetries VII: Parabasal optics as Lorentz transformations

Abstract

In the usual view the parabasal optics of a general optical system (i.e., a system that need have no symmetries) is represented by an element of the group of symplectic transformations Sp(2). An alternative representation, namely, by elements of the five-dimensional Lorentz group SO(3,2) is considered here. A particular case is that of the r-symmetric system. Its symmetry entails a degeneracy of the formalism in which the lower-dimensional Lorentz group SO(1, 2) takes the place of SO(3,2).