{
  "abstract": "This PhD thesis constructs the $P(Φ)_2$ Euclidean quantum field theory on $\\mathscr{S}'(\\mathbb{R}^2)$. We first construct the finite-volume measure of the $P(Φ)_2$ model on $\\mathscr{D}'(\\mathbb{S}_R)$, where $\\mathbb{S}_R$ is a two-dimensional sphere of radius $R\\in\\mathbb{N}_+$. To this end, we rely on Nelson's hypercontractivity estimate. We then use parabolic stochastic quantization and the energy method to construct the infinite-volume measure on $\\mathscr{S}'(\\mathbb{R}^2)$. This requires establishing the global-in-time existence of solutions to the corresponding stochastic partial differential equations with fixed cutoffs. The remainder of the thesis is devoted to verifying the Osterwalder-Schrader axioms: regularity, reflection positivity, and invariance under translations, rotations, and reflections. This combination of axioms, which is crucial for obtaining a non-trivial local relativistic quantum field theory on Minkowski spacetime, had not been established in earlier constructions based on stochastic quantization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34063",
  "author_total": 1,
  "authors": [
    {
      "name": "Azam Jahandideh"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/25s61sxcpnjy6.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34063",
  "fulltext_url": null,
  "id": "25s61sxcpnjy6",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34063",
  "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.PR"
    ],
    [
      "openalex",
      "2610|advanced mathematical theories"
    ]
  ],
  "openalex": "W7167766733",
  "pdf_url": "https://arxiv.org/pdf/2610.34063",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/25s61sxcpnjy6.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:35Z",
      "native_id": "2610.34063",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34063"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.PR",
      "subfield": "probability"
    }
  ],
  "title": "Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models",
  "title_text": "Stochastic quantization and Osterwalder-Schrader axioms for quantum field theory models",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/25s61sxcpnjy6",
  "venue": "arXiv",
  "versions": []
}