Discrete space-time symmetry, polarization eigenmodes and their degeneracies

TL;DR

This paper explores how discrete space-time symmetries and group theory can classify polarization eigenmodes and degeneracies in magnetic crystals, offering a topological perspective without relying on tensor expansions.

Contribution

It introduces a group-theoretic framework using C4 and V groups to analyze polarization modes and their degeneracies in magnetic media.

Findings

Polarization eigenmodes are classified by irreducible representations of C4×V.

Degeneracies are explained through the symmetry properties of the finite Abelian group.

The approach provides qualitative insights into gyrotropy without tensor truncation.

Abstract

The irreducible representations of the group C4(direct product)V can be used to distinguish polarization eigenmodes, to account for their degeneracies and to associate them with particular magnetic crystal classes. The occurrence of this finite Abelian group points to a possible connection with topology but, irrespective of this, qualitative features of gyrotropy in condensed media can be approached in a way that does not depend on arbitrarily truncated tensor expansions.