{
  "abstract": "We propose a second-order partial differential equation method to solve multi-loop Feynman integrals as an equilibrium problem. As a proof-of-concept demonstration, we perform a Galerkin discretization of the corresponding variational form and employ the finite element method to compute two-loop four-point Feynman integrals. This method can solve the integral over a broad region of multi-dimensional phase space once and for all. This work establishes a new connection between perturbative quantum field theory and modern partial differential equation methods, with the potential to streamline a wide range of phenomenological applications.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2607.18406",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiang Chen"
    },
    {
      "name": "Hantian Zhang"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/72ydgdhthkzjx.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2607.18406",
  "fulltext_url": null,
  "id": "72ydgdhthkzjx",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2607.18406",
  "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-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7170041640",
  "pdf_url": "https://arxiv.org/pdf/2607.18406",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72ydgdhthkzjx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2607.18406",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2607.18406"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Feynman Integrals Meet Second-Order Partial Differential Equations",
  "title_text": "Feynman Integrals Meet Second-Order Partial Differential Equations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/72ydgdhthkzjx",
  "venue": "arXiv",
  "versions": []
}