Kramers degeneracy without eigenvectors

TL;DR

This paper presents an algebraic approach to Kramers degeneracy that does not depend on the existence of eigenvectors, broadening its applicability to more quantum systems.

Contribution

It introduces a novel algebraic framework for Kramers degeneracy, removing the eigenvector assumption from Wigner's original proof.

Findings

Kramers degeneracy can be established algebraically without eigenvectors

The new approach applies to quantum systems where Hamiltonians lack eigenvectors

Provides a more general proof of Kramers degeneracy in time-reversal invariant systems

Abstract

Wigner gave a well-known proof of Kramers degeneracy, for time reversal invariant systems containing an odd number of half-integer spin particles. But Wigner's proof relies on the assumption that the Hamiltonian has an eigenvector, and thus does not apply to many quantum systems of physical interest. This note illustrates an algebraic way to talk about Kramers degeneracy that does not appeal to eigenvectors, and provides a derivation of Kramers degeneracy in this more general context.