{
  "abstract": "We construct and analyze a renormalized three-dimensional massive Lee model; its renormalized Hamiltonian is defined intrinsically through an abstract construction which explicitly provides the operator domain, action and a Kre\\uın-like resolvent formula. Conservation of the total excitation number reduces the spectral analysis of the full Hamiltonian to a sector-wise study of the spectral profile of an explicit operator pencil, playing the role of an operator-valued Weyl function. We construct essential spectrum components in a sector generated by lower excitation sectors and obtain the inclusion in the expected sector-wise HVZ type formula; the full formula is proved in the first two sectors and, under explicit conditions, in every sector. Below the free or one-excitation threshold, the point spectrum in every higher sector is described by a bounded self-adjoint nonnegative Birman--Schwinger operator. In every sector with at least two excitations we prove absence of sub-threshold spectrum for arbitrary coupling when the renormalized gap is not smaller than the boson mass, and under an explicit weak-coupling condition when it is smaller. In the latter case we also derive a sufficient condition for the existence of a simple bound state in the two-excitation sector.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.34980",
  "author_total": 4,
  "authors": [
    {
      "name": "Claudio Cacciapuoti"
    },
    {
      "name": "Federica Muscolino"
    },
    {
      "name": "Diego Noja"
    },
    {
      "name": "Andrea Posilicano"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/01a21bcw6dcgq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.34980",
  "fulltext_url": null,
  "id": "01a21bcw6dcgq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.34980",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214780740",
  "pdf_url": "https://arxiv.org/pdf/2609.34980",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/01a21bcw6dcgq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:12Z",
      "native_id": "2609.34980",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.34980"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "A renormalized Lee Model: resolvent and spectral analysis",
  "title_text": "A renormalized Lee Model: resolvent and spectral analysis",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:17Z",
  "url": "https://research.draconitic.com/paper/01a21bcw6dcgq",
  "venue": "arXiv",
  "versions": []
}