Lorentz Group in Condensed Matter Physics

Abstract

It is shown that the Lorentz group plays prominent roles in at least two areas in condensed matter physics, namely in the Bogoliubov transformation and optical filters. It is pointed out that the underlying symmetry of the Bogoliubov transformation is that of two coupled oscillators, and that the underlying symmetry of two coupled oscillators in that of the group $O(3,3)$. The Lorentz group is also shown to be the underlying symmetry group for the Jones matrix formalism which is standard language for optical filters.