{
  "abstract": "Building on the established one-particle formula for the Araki relative entropy of coherent states, we study how its value acquires a nontrivial dependence on the mass of the scalar field. For a localized vector $h$ belonging to the standard subspace $H_m$ of the one-particle Hilbert space, the known quadratic-form expression is: $S_{H_m}(h)=-\\langle h,\\logδ_{H_m}\\,h\\rangle$. Our contribution is to construct explicitly a mass-indexed family of vectors of the wedge standard subspace on which this expression is evaluated. The mass-shell map $h_m=E_mf$ organizes four structural conditions on rapidity representatives---on-shell dependence, a controlled massless boundary value, decay for large real rapidity, and Bisognano--Wichmann strip analyticity---and we exhibit an entire rapidity wave function, built from a doubled light-cone phase, two sinc factors, and a Gaussian pair, that satisfies them together with the sharp localization criterion: Hardy-type $L^2$ control throughout the Bisognano--Wichmann strip and the exact Tomita boundary relation. The family therefore belongs to $H_m(\\W_R)$ for every $m>0$, and its Araki relative entropy is finite and strictly positive, with an exact spectral representation that makes positivity manifest. The entropy is strongly suppressed at large mass, attains a maximum at intermediate mass in $1+1$ dimension, and converges to a finite value along the modular flow as $m\\to0^+$. The construction extends fiberwise to $1{+}d$ dimensions through the transverse mass.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.12676",
  "author_total": 3,
  "authors": [
    {
      "name": "M. S. Guimaraes"
    },
    {
      "name": "I. Roditi"
    },
    {
      "name": "S. P. Sorella"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/da0kg9hzmy4rc.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.12676",
  "fulltext_url": null,
  "id": "da0kg9hzmy4rc",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.12676",
  "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",
      "hep-th"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "quant-ph"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7213100044",
  "pdf_url": "https://arxiv.org/pdf/2609.12676",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/da0kg9hzmy4rc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:07Z",
      "native_id": "2609.12676",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.12676"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:hep-th",
      "subfield": "high-energy"
    },
    {
      "field": "physics",
      "origin": "arxiv:quant-ph",
      "subfield": "quantum"
    }
  ],
  "title": "Mass Dependence of Araki Relative Entropy through Modular Theory",
  "title_text": "Mass Dependence of Araki Relative Entropy through Modular Theory",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:11Z",
  "url": "https://research.draconitic.com/paper/da0kg9hzmy4rc",
  "venue": "arXiv",
  "versions": []
}