{
  "annotation_id": "6b72b206-d1c7-4177-805b-f4c5ae0f1d82",
  "date_created": "2026-03-02T18:02:40.450000Z",
  "date_modified": "2026-03-02T18:02:40.450000Z",
  "file_hash": "3b28e6b73f2d48a5cc1a5ba40fea6fb4eb45111ad10d648c61fe28e6433b6b3a",
  "private": false,
  "record": {
    "abstract": "For Dirac equation, operator-invariants containing explicit time-dependence\nin parallel to known time-dependent invariants of nonrelativistic Schr\\\"odinger\nequation are introduced and discussed. As an example, a free Dirac particle is\nconsidered and new invariants are constructed for it. The integral of motion,\nwhich is initial Newton-Wigner position operator, is obtained explicitly for a\nfree Dirac particle. For such particle with kick modeled by delta-function of\ntime, the time-depending integral, which has physical meaning of initial\nmomentum, is found.",
    "arxiv_id": "quant-ph/9702035",
    "authors": [
      "V. I. Man\u0027ko",
      "R. V. Mendes"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0031-8949/56/5/001",
    "title": "Time-Dependent Invariants for Dirac Equation and Newton-Wigner Position   Operator",
    "url": "https://arxiv.org/abs/quant-ph/9702035"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "a002353e-02da-41fd-b6f1-c6d7865e510d",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}