{
  "abstract": "We consider the ground state energy E_0(alpha, Lambda) of a single spinless non-relativistic electron coupled to the quantized radiation field with a sharp ultraviolet cutoff Lambda (the Pauli-Fierz model), with fine structure constant alpha = e^2/(4 pi). Lieb and Loss proved that C_1 alpha^(1/2) Lambda^(3/2) <= E_0 <= C_2 alpha^(2/7) Lambda^(12/7) for large Lambda and suggested that the upper bound, which comes from product states, gives the correct order. We prove that, for every fixed alpha > 0, E_0(alpha, Lambda) = (1+o(1)) c_alpha alpha^(2/7) Lambda^(12/7) as Lambda -> infinity, with an explicit constant c_alpha = 0.99338...; more generally, this holds uniformly in the joint limit Lambda/alpha -> infinity, alpha^(5/2) Lambda -> infinity, provided log(2+alpha) = o((Lambda/alpha)^(1/21)). Since our upper bound holds already for the infimum over product states, it follows that the ratio of E_0 to this infimum tends to one: electron-field correlations do not contribute to the leading term. The condition alpha^(5/2) Lambda -> infinity cannot be dropped, since for alpha^(5/2) Lambda -> 0 the vacuum trial state gives a smaller energy. The upper bound follows from a coherent state bound for the field energy in a fixed electron density. The lower bound combines a periodization of the field, a Born-Oppenheimer bound in which phase multiplication and a Hardy inequality in field space are applied block by block, and a lower bound on the magnetic Neumann Laplacian on a cube for band-limited fields; the key point of the last is that a band-limited field obeying a weighted gradient condition cannot concentrate its vorticity.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34122",
  "author_total": 1,
  "authors": [
    {
      "name": "Shinichiro Futakuchi"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b9byx099t45fw.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34122",
  "fulltext_url": null,
  "id": "b9byx099t45fw",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34122",
  "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": "W7223872749",
  "pdf_url": "https://arxiv.org/pdf/2610.34122",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b9byx099t45fw.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34122",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34122"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.SP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "The sharp leading asymptotics of the self-energy of the spinless Pauli-Fierz model",
  "title_text": "The sharp leading asymptotics of the self-energy of the spinless Pauli-Fierz model",
  "type": "preprint",
  "updated_at": "2026-11-05T15:20:22Z",
  "url": "https://research.draconitic.com/paper/b9byx099t45fw",
  "venue": "arXiv",
  "versions": []
}