{
  "annotation_id": "be879eec-4481-4db4-9c86-047c0ef31797",
  "date_created": "2026-03-02T18:01:52.684000Z",
  "date_modified": "2026-03-02T18:01:52.684000Z",
  "file_hash": "7730d83d3565b7b48796fd1e35f3c6078d4232bd916d7ab72ce95b24a6da3ad2",
  "private": false,
  "record": {
    "abstract": "A formulation of quantum mechanics with additive and multiplicative\n(q-)difference operators instead of differential operators is studied from\nfirst principles. Borel-quantisation on smooth configuration spaces is used as\nguiding quantisation method. After a short discussion this method is translated\nstep-by-step to a framework based on difference operators. To restrict the\nresulting plethora of possible quantisations additional assumptions motivated\nby simplicity and plausibility are required. Multiplicative difference\noperators and the corresponding q-Borel kinematics are given on the circle and\nits N-point discretisation; the connection to q-deformations of the Witt\nalgebra is discussed. For a \"natural\" choice of the q-kinematics a\ncorresponding q-difference evolution equation is obtained. This study shows\ngeneral difficulties for a generalisation of a physical theory from a known one\nto a \"new\" framework.",
    "arxiv_id": "quant-ph/0207077",
    "authors": [
      "V. K. Dobrev",
      "H. -D. Doebner",
      "R. Twarock"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1016/S0034-4877(02)80069-6",
    "journal_ref": "Rep. Math. Phys. 50 (2002) 409-431",
    "title": "Quantum Mechanics with Difference Operators",
    "url": "https://arxiv.org/abs/quant-ph/0207077"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "4eadc909-2865-4852-935b-9109bde1c6bc",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}