{
  "abstract": "We study the linearized Boltzmann collision operator for three-dimensional hard spheres and reorganize the complete operator so that its angular and radial structures are explicit before any Sonine truncation. From the Carleman representation, the collision integral becomes a superposition of orthogonal translations; in Hermite/Fock and Bargmann form these generate a single analytic coherent-state kernel for all Hermite collision brackets. Rotational covariance separates fixed angular-momentum sectors, each reducing exactly to a one-variable radial Bargmann space with an $\\mathfrak{su}(1,1)$ structure. The radial operator is $\\mathfrak A_\\ell=κπG(\\mathcal J_\\ell)-\\mathfrak C_\\ell$, where $\\mathcal J_\\ell$ is an explicit Laguerre--Jacobi operator and $\\mathfrak C_\\ell$ is compact. A unitary intertwiner identifies this realization with the classical Burnett/Sonine coordinate, recovering the Burnett matrix and standard stress and heat-flux corrections. For the untruncated operator, the compact gain gives only compact corrections, while the loss sets the common essential spectrum $[ν_{\\min},\\infty)$. Radially squeezed $\\mathfrak{su}(1,1)$ coherent packets yield threshold Weyl sequences in every fixed angular sector. With $\\ell\\to\\infty$ and squeezing scaled as $\\ell^{-1}$, they furnish full-space Weyl sequences throughout the essential band interior, with $\\langle j\\rangle\\sim\\ell^2$, revealing quadratic continuum corridors in the $(\\ell,j)$ plane. At fixed $\\ell$ and $j\\to\\infty$, the matrix tail approaches a universal Toeplitz operator whose zero at $θ=π$ is the local signature of the same threshold escape. Thus the Fock reformulation provides exact radialization and constructive control of the global spectral geometry.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09548",
  "author_total": 1,
  "authors": [
    {
      "name": "Ilya Karlin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/99cmmpz0rw15a.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09548",
  "fulltext_url": null,
  "id": "99cmmpz0rw15a",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09548",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2604|Gas Dynamics and Kinetic Theory"
    ]
  ],
  "openalex": "W7212122549",
  "pdf_url": "https://arxiv.org/pdf/2609.09548",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/99cmmpz0rw15a.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09548",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09548"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Bargmann-Fock Representation and Global Estimates for the Linearized Hard-Sphere Boltzmann Operator",
  "title_text": "Bargmann-Fock Representation and Global Estimates for the Linearized Hard-Sphere Boltzmann Operator",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/99cmmpz0rw15a",
  "venue": "arXiv",
  "versions": []
}