{
  "abstract": "Dereziński and Gérard constructed the Gaussian $β$-Markov path space of a free Bose field in a form equivalent to the Araki--Woods representation, which suits nonequilibrium statistical mechanics with a quantum-field environment, but only for one-particle Hamiltonians with a spectral gap. We extend this construction, together with the equivalence to the Araki--Woods representation, to one-particle Hamiltonians without a spectral gap. For one-particle Hamiltonians joined by isometric embeddings that intertwine their spectral measures and test spaces, as for nested momentum lattices, and for compatible regularizers, the path spaces form a projective system whose limit carries the time translations and the reflection, which gives a quasi-local construction. The extension is intended for constructive quantum field theory at positive temperature and equilibrium statistical mechanics, for instance in the problem of the absence of Bose--Einstein condensation of quasiparticles whose number is not conserved.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34783",
  "author_total": 1,
  "authors": [
    {
      "name": "Yoshitsugu Sekine"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/38xqnswd96ptj.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34783",
  "fulltext_url": null,
  "id": "38xqnswd96ptj",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34783",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "openalex",
      "2610|Advanced Operator Algebra Research"
    ]
  ],
  "openalex": "W7223873499",
  "pdf_url": "https://arxiv.org/pdf/2610.34783",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/38xqnswd96ptj.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34783",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34783"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Gaussian $β$-Markov Path Spaces without a Spectral Gap and the Araki--Woods Representations",
  "title_text": "Gaussian β-Markov Path Spaces without a Spectral Gap and the Araki--Woods Representations",
  "type": "preprint",
  "updated_at": "2026-11-09T00:20:28Z",
  "url": "https://research.draconitic.com/paper/38xqnswd96ptj",
  "venue": "arXiv",
  "versions": []
}