{
  "annotation_id": "4662d662-9bc4-4bc3-8255-586338d68222",
  "date_created": "2026-03-02T18:01:04.338000Z",
  "date_modified": "2026-03-02T18:01:04.338000Z",
  "file_hash": "917b83c7e1c5171eb630d7ebeb2cc37e6c5a1fea52822682d006122ab138d4dd",
  "private": false,
  "record": {
    "abstract": "We discuss the structure of the two- and three-body T-matrices, scattering\nmatrices, and resolvents continued to the unphysical energy sheets. Our\nconclusions arise due to the representations that have been found for\nanalytically continued momentum-space kernels of the T-operators. These\nrepresentations are explicitly written only in terms of the physical-sheet\nkernels of the T-matrix itself. One of advantages of the representations in the\nthree-body case is that they show which portions of the physical-sheet\nthree-body scattering matrix are ``responsible\u0027\u0027 for the resonances associated\nwith a particular unphysical sheet. A resonance appears to be the energy where\nthe correspondingly truncated scattering matrix (taken on the physical sheet)\nhas eigenvalue zero. We also mention applications of this approach to some\nspecific three-body systems, based on the Faddeev differential equations.",
    "arxiv_id": "physics/0511238",
    "authors": [
      "Alexander K. Motovilov"
    ],
    "categories": [
      "physics.atm-clus",
      "math-ph",
      "math.MP",
      "nucl-th"
    ],
    "doi": "10.1007/s00601-005-0134-y",
    "journal_ref": "Few Body Systems, Vol. 38 (2006) 115-120",
    "title": "Explicit Representations for the T-Matrix on Unphysical Energy Sheets   and Resonances in Two- and Three-Body Systems",
    "url": "https://arxiv.org/abs/physics/0511238"
  },
  "schema_id": "dorsal/arxiv",
  "source": {
    "execution_id": "5d5691fc-2ec5-44d9-a6e8-34da03c4ad6b",
    "id": "arXiv Dataset IDs",
    "type": "Model",
    "variant": "snapshot-2026-03-01",
    "version": "0.1.0"
  },
  "user_id": 1000002
}