Lorentz Group in Condensed Matter Physics

TL;DR

This paper explores how the Lorentz group underpins key concepts in condensed matter physics, specifically in Bogoliubov transformations and optical filter formalism, revealing deep symmetry connections.

Contribution

It demonstrates the role of the Lorentz group as a fundamental symmetry in both Bogoliubov transformations and optical filter representations in condensed matter physics.

Findings

Lorentz group symmetry in Bogoliubov transformations

Underlying symmetry of coupled oscillators is O(3,3)

Lorentz group as the symmetry of Jones matrix formalism

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.