{
  "annotation_id": "4a8a73a5-66c9-4eb9-bf78-cf6f483c32c2",
  "date_created": "2026-03-02T18:02:38.021000Z",
  "date_modified": "2026-03-02T18:02:38.021000Z",
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  "record": {
    "abstract": "The momentum operator for a particle in a box is represented by an infinite\norder Hermitian matrix $P$. Its square $P^2$ is well defined (and diagonal),\nbut its cube $P^3$ is ill defined, because $P P^2\\neq P^2 P$. Truncating these\nmatrices to a finite order restores the associative law, but leads to other\ncurious results.",
    "arxiv_id": "quant-ph/9412007",
    "authors": [
      "Ofir E. Alon",
      "Nimrod Moiseyev",
      "Asher Peres"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1088/0305-4470/28/6/027",
    "journal_ref": "J.Phys. A28 (1995) 1765-1770",
    "title": "Infinite matrices may violate the associative law",
    "url": "https://arxiv.org/abs/quant-ph/9412007"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "2cd080fc-02ef-4c8a-8ea2-f997e9ecf6ab",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}