ExactPT-symmetry is equivalent to Hermiticity

2003/04/30 by Ali Mostafazadeh · 8 citations
Mathematics · Physics and Astronomy · #Nonlinear Waves and Solitons #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Non-Hermitian Physics #hep-th #math-ph #math.MP #quant-ph

paper · pdf · doi:10.1088/0305-4470/36/25/312

published as J.Phys.A36:7081-7092,2003 · Few typos have been corrected and a reference updated

openalex publication_date 2003/06/11 · arxiv created 2003/06/23 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/31

Abstract

We show that a quantum system possessing an exact antilinear symmetry, in particular PT -symmetry, is equivalent to a quantum system having a Hermitian Hamiltonian. We construct the unitary operator relating an arbitrary non-Hermitian Hamiltonian with exact PT -symmetry to a Hermitian Hamiltonian. We apply our general results to PT -symmetry in finite dimensions and give the explicit form of the above-mentioned unitary operator and Hermitian Hamiltonian in two dimensions. Our findings lead to the conjecture that non-Hermitian CPT -symmetric field theories are equivalent to certain nonlocal Hermitian field theories.

Citations

• All Hermitian Hamiltonians have parity
• Pseudo-Hermiticity of Hamiltonians under imaginary shift of the coordinate: real spectrum of complex potentials

Cited by

• Solitons in a Hamiltonian P T -symmetric coupler
• Equivalent Hamiltonian for the Lee model
• LocalPTSymmetry Violates the No-Signaling Principle
• Some spectral equivalences between Schrödinger operators
• Exactly solvablePT-symmetric Hamiltonian having no Hermitian counterpart
• An algebraic PT-symmetric quantum theory with a maximal mass
• PT/non-PT symmetric and non-Hermitian Pöschl–Teller-like solvable potentials via Nikiforov–Uvarov method
• \mathcal P\mathcal T symmetry as a generalization of Hermiticity