2002/09/06 by Stefan Weigert · 1 citation
Mathematics · Physics and Astronomy · #Complex conjugate #Eigenvalues and eigenvectors #Energy spectrum #Irreducible representation #Nonlinear Waves and Solitons #Operator (biology) #Quantum Mechanics and Non-Hermitian Physics #Spectral Theory in Mathematical Physics #Spectral properties #Spectrum (functional analysis) #Symmetry (geometry) #quant-ph
paper · pdf · doi:10.1088/1464-4266/5/3/380
published as J. Opt. B 5 (2003) S416 · 8 pages
arxiv created 2002/09/06 · openalex publication_date 2003/06/01 · arxiv updated 2009/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
The impact of an anti-unitary symmetry on the spectrum of non-Hermitian operators is studied. Wigner’s normal form of an anti-unitary operator accounts for the spectral properties of non-Hermitian, 𝒫𝒯-symmetric Hamiltonians. The occurrence of either single real or complex conjugate pairs of eigenvalues follows from this theory. The corresponding energy eigenstates span either one-or two-dimensional irreducible representations of the symmetry 𝒫𝒯. In this framework, the concept of a spontaneously broken 𝒫𝒯-symmetry is not needed.