{
  "annotation_id": "7c54d7b4-468a-4fe4-8a7b-db03958f3515",
  "date_created": "2026-03-02T18:02:24.195000Z",
  "date_modified": "2026-03-02T18:02:24.195000Z",
  "file_hash": "784df2ceb90a7ec36a26547ed7ebe637a8c4d372fec6614d918106476e81d658",
  "private": false,
  "record": {
    "abstract": "An extensively tacit understandings of equivalency between the deformed\nHeisenberg-Weyl algebra in noncommutative space and the undeformed\nHeisenberg-Weyl algebra in commutative space is elucidated. Equivalency\nconditions between two algebras are clarified. It is explored that the deformed\nalgebra related to the undeformed one by a non-orthogonal similarity\ntransformation. Furthermore, non-existence of a unitary similarity\ntransformation which transforms the deformed algebra to the undeformed one is\ndemonstrated. The un-equivalency theorem between the deformed and the\nundeformed algebras is fully proved. Elucidation of this un-equivalency theorem\nhas basic meaning both in theory and practice.",
    "arxiv_id": "quant-ph/0602179",
    "authors": [
      "Jian-Zu Zhang"
    ],
    "categories": [
      "quant-ph"
    ],
    "title": "Un-equivalency Theorem of Deformed Heisenberg-Weyl\u0027s Algebra in   Noncommutative Space",
    "url": "https://arxiv.org/abs/quant-ph/0602179"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "91c03fc5-8562-40fb-911c-a3770e4c2ebe",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}