{
  "annotation_id": "48da485a-c353-4b2f-b566-5a45eeb40657",
  "date_created": "2026-03-02T18:01:28.003000Z",
  "date_modified": "2026-03-02T18:01:28.003000Z",
  "file_hash": "1f72219a4fd5f178147f8761e981f8cf2a7c84c543de9f53623a5fa58f038898",
  "private": false,
  "record": {
    "abstract": "We prove the formula for the traces of certain class of operators in bosonic\nand fermionic Fock spaces. Vertex operators belong to this class. Traces of\nvertex operators can be used for calculation of correlation functions and\nformfactors of integrable models (XXZ, Sine-Gordon, etc.), that is why we are\ninterested in this problem. Also we show that Fredholm\u0027s minor and determinant\ncan be expressed by such traces. We obtain a short proof of the Fredholm\u0027s\nformula for the solution of an integral equation. Analogue of Fredholm\u0027s\nformula in terms of permanents is obtained.",
    "arxiv_id": "q-alg/9703017",
    "authors": [
      "Alexander Chervov"
    ],
    "categories": [
      "q-alg",
      "funct-an",
      "hep-th",
      "math.FA",
      "math.QA"
    ],
    "title": "Traces of creation-annihilation operators and Fredholm\u0027s formulas",
    "url": "https://arxiv.org/abs/q-alg/9703017"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "f0296ce9-8ebd-4e03-882d-4b1e861db046",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}