Metaplectic group and Fourier optics

Abstract

The evolution of a light wave along an optical system, in paraxial approximation, can be described with the aid of a group of operators acting as canonical transformations in the framework of nonrelativistic quantum mechanics in two dimensions. This group is isomorphic to the ten-dimensional metaplectic group Mp(2). The homomorphism Mp(2)\ensuremath{\rightarrow}Sp(2) (symplectic group) gives a description of the geometrical-optics approximation.