{
  "annotation_id": "1173ca8c-1331-4fa7-bf00-5ec4c79d1636",
  "date_created": "2026-03-02T18:02:19.749000Z",
  "date_modified": "2026-03-02T18:02:19.749000Z",
  "file_hash": "6809b7d56a48a8112c1e8a5336396a06e1d30e5acaf0f435641e01daa33db9fa",
  "private": false,
  "record": {
    "abstract": "Using the bicomplex numbers $\\mathbb{T}$ which is a commutative ring with\nzero divisors defined by $\\mathbb{T}=\\{w_0 + w_1 i_1 + w_2 i_2 + w_3 j | w_0,\nw_1, w_2, w_3 \\in \\mathbb{R}\\}$ where $i_{1}^{2} = -1, i_{2}^{2} = -1, j^2 = 1,\ni_1 i_2 = j = i_2 i_1$, we construct hyperbolic and bicomplex Hilbert spaces.\nLinear functionals and dual spaces are considered and properties of linear\noperators are obtained; in particular it is established that the eigenvalues of\na bicomplex self-adjoint operator are in the set of hyperbolic numbers.",
    "arxiv_id": "quant-ph/0510203",
    "authors": [
      "Dominic Rochon",
      "Sebastien Tremblay"
    ],
    "categories": [
      "quant-ph"
    ],
    "doi": "10.1007/s00006-006-0008-5",
    "journal_ref": "Advances in Applied Clifford Algebras, 2006, Volume 16, Issue 2,\n  pp 135-157",
    "title": "Bicomplex Quantum Mechanics: II. The Hilbert Space",
    "url": "https://arxiv.org/abs/quant-ph/0510203"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "3474e089-7ea0-4c7f-b3fd-6d3f097e0ef3",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}