{
  "annotation_id": "2000313c-a626-4415-8d81-18690833def0",
  "date_created": "2026-03-02T18:02:13.514000Z",
  "date_modified": "2026-03-02T18:02:13.514000Z",
  "file_hash": "b94fcf777670b8df215bd59f160cb1b9cded0115151cd4cfc642381ac6e78b80",
  "private": false,
  "record": {
    "abstract": "In most introductory courses on quantum mechanics one is taught that the\nHamiltonian operator must be Hermitian in order that the energy levels be real\nand that the theory be unitary (probability conserving). To express the\nHermiticity of a Hamiltonian, one writes $H=H^\\dagger$, where the symbol\n$\\dagger$ denotes the usual Dirac Hermitian conjugation; that is, transpose and\ncomplex conjugate. In the past few years it has been recognized that the\nrequirement of Hermiticity, which is often stated as an axiom of quantum\nmechanics, may be replaced by the less mathematical and more physical\nrequirement of space-time reflection symmetry (PT symmetry) without losing any\nof the essential physical features of quantum mechanics. Theories defined by\nnon-Hermitian PT-symmetric Hamiltonians exhibit strange and unexpected\nproperties at the classical as well as at the quantum level. This paper\nexplains how the requirement of Hermiticity can be evaded and discusses the\nproperties of some non-Hermitian PT-symmetric quantum theories.",
    "arxiv_id": "quant-ph/0501052",
    "authors": [
      "Carl M. Bender"
    ],
    "categories": [
      "quant-ph",
      "hep-th"
    ],
    "doi": "10.1080/00107500072632",
    "journal_ref": "Contemp.Phys.46:277-292,2005",
    "title": "Introduction to PT-Symmetric Quantum Theory",
    "url": "https://arxiv.org/abs/quant-ph/0501052"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4910c343-7318-4942-9d1b-13ec38e147b9",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}