{
  "annotation_id": "16db2b2c-ca41-45e2-99f1-84b0e3e4122e",
  "date_created": "2026-03-02T18:01:27.748000Z",
  "date_modified": "2026-03-02T18:01:27.748000Z",
  "file_hash": "5c12580bd2607e363eeb37173d9ca8f36d614e5ebe29d37ad18ed7ea8eff8862",
  "private": false,
  "record": {
    "abstract": "We extend the theory of diffeomorphism-invariant spin network states from the\nreal-analytic category to the smooth category. Suppose that G is a compact\nconnected semisimple Lie group and P -\u003e M is a smooth principal G-bundle. A\n`cylinder function\u0027 on the space of smooth connections on P is a continuous\ncomplex function of the holonomies along finitely many piecewise smoothly\nimmersed curves in M. We construct diffeomorphism-invariant functionals on the\nspace of cylinder functions from `spin networks\u0027: graphs in M with edges\nlabeled by representations of G and vertices labeled by intertwining operators.\nUsing the `group averaging\u0027 technique of Ashtekar, Marolf, Mourao and Thiemann,\nwe equip the space spanned by these `diffeomorphism-invariant spin network\nstates\u0027 with a natural inner product.",
    "arxiv_id": "q-alg/9708005",
    "authors": [
      "John C. Baez",
      "Stephen Sawin"
    ],
    "categories": [
      "q-alg",
      "gr-qc",
      "math.QA"
    ],
    "journal_ref": "Jour. Funct. Analysis, 158 (1998) 253-266",
    "title": "Diffeomorphism-Invariant Spin Network States",
    "url": "https://arxiv.org/abs/q-alg/9708005"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "ec397bd6-866f-472d-96cc-eaed232ea280",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}