{
  "annotation_id": "064cf860-39cf-4c4f-8c1a-d3707129c7e7",
  "date_created": "2026-03-02T18:01:51.838000Z",
  "date_modified": "2026-03-02T18:01:51.838000Z",
  "file_hash": "a9e0f05f45b57434bec1cef2ca89b26960de1625cb7b4e8115a0ef1c9e3d5b89",
  "private": false,
  "record": {
    "abstract": "In Ukrain. J. Phys., 1967, V.12, N 5, p.741-746 it was shown how, for a given\n(discrete) mass spectrum of elementary or hypothetical particles, it was\npossible to construct a non-trivial algebra G containing a Poincare algebra P\nas a subalgebra so that the mass operator, defined throughout the space where\none of the irreducible representations G is given, is self-conjugate and its\nspectrum coincides with the given mass spectrum. Such an algebra was\nconstructed in explicit form for the nonrelativistic case, i.e., the generators\nwere written for the algebra. However, the problem of how to assign the algebra\nG constructively and determine an explicit form of the mass operator in the\nrelativistic case has remained unsolved. In the present work we present a\nsolution of this problem, construct continuum analogs of the classical algebras\nU(N) and Sp(2N), and show that the problem of including the Poincare algebra\ncan be formulated in the language of wave function equations.",
    "arxiv_id": "quant-ph/0206056",
    "authors": [
      "Wilhelm I. Fushchych"
    ],
    "categories": [
      "quant-ph",
      "math-ph",
      "math.MP",
      "nlin.SI"
    ],
    "journal_ref": "Ukr.J.Phys. 13 (1968) 256-262",
    "title": "A relativistically invariant mass operator",
    "url": "https://arxiv.org/abs/quant-ph/0206056"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "797e33d3-5d3b-43f5-9066-a2c29ab8633c",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}