{
  "annotation_id": "5593f4c2-02be-4044-8990-651b086be2c1",
  "date_created": "2026-03-02T18:01:39.208000Z",
  "date_modified": "2026-03-02T18:01:39.208000Z",
  "file_hash": "024811db15ef9feae3fae6fa86a991200f18b9b12c736b09df26821dfd292f70",
  "private": false,
  "record": {
    "abstract": "The quantum state of a particle can be completely specified by a position at\none instant of time. This implies a lack of information, hence a symmetry, as\nto where the particle will move. We here study the consequences for free\nparticles of spin 0 and spin 1/2. On a cubic spatial lattice a hopping equation\nis derived, and the continuum limit taken. Spin 0 leads to the Schroedinger\nequation, and spin 1/2 to the Weyl equation. Both Hamiltonians are hermitian\nautomatically, if time-reversal symmetry is assumed. Hopping amplitudes with a\n\"slight\" inhomogeneity lead to the Weyl equation in a metric-affine space-time.",
    "arxiv_id": "quant-ph/0005051",
    "authors": [
      "L. Polley"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Position eigenstates, symmetries, and the redundant hermiticity of   free-particle Hamiltonians",
    "url": "https://arxiv.org/abs/quant-ph/0005051"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ce2277f8-aa58-4943-8282-42b193e1d83b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}