{
  "abstract": "We formulate and prove existence of pure quasifree Hadamard states for the Klein--Gordon field with Dirichlet boundary condition on a globally hyperbolic spacetime with timelike boundary. The microlocal condition is imposed on the one-particle Hilbert-space-valued distribution $p\\circ G_D$ rather than on the two-point function. This is expressed by a $b$-wave-front set condition on the compressed future cone. The analysis on the manifold with corners $\\bar M\\times\\bar M$ is then almost completely avoided. We prove that our version of the Hadamard condition is universal in the class of quasi-free Hadamard states. We also prove a propagation theorem for positive-energy microlocal splittings which uses only a microlocal splitting in the small $b$-calculus and well-posedness of the Dirichlet problem, and in particular requires no propagation theorem for reflected or gliding rays; combined with an explicit computation in the ultrastatic case and a Fulling--Narcowich--Wald deformation argument this yields the construction of a pure quasi-free Dirichlet--Hadamard state.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.13358",
  "author_total": 2,
  "authors": [
    {
      "name": "Alessandro Pietro Contini"
    },
    {
      "name": "Alexander Strohmaier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qgq5ft1c2bgk.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.13358",
  "fulltext_url": null,
  "id": "7qgq5ft1c2bgk",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.13358",
  "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.AP"
    ],
    [
      "arxiv",
      "math.MP"
    ],
    [
      "arxiv",
      "math.SP"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.13358",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-11",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qgq5ft1c2bgk.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.13358",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.13358"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.AP",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Hadamard states for spacetimes with timelike boundaries",
  "title_text": "Hadamard states for spacetimes with timelike boundaries",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/7qgq5ft1c2bgk",
  "venue": "arXiv",
  "versions": []
}