{
  "abstract": "We study classical Maxwell fields with non-trivial sources in four-dimensional Minkowski spacetime. In particular, contact and symplectic geometric aspects are discussed. As a point of departure, it is shown that a few classes of solutions with sources are constructed from the so-called Beltrami fields, where these fields are contact forms on three-dimensional Riemannian manifolds. In addition, several applications in these classes are provided. One is to give a solution to the London equations for superconductors. Another one is that, if there is a non-trivial conserved quantity along the magnetic vector field, then the Maxwell system can be viewed as a Liouville integrable Hamiltonian system on a four-dimensional symplectic manifold, where this manifold is obtained by a symplectization of the contact manifold. As examples, Maxwell fields with the Lundquist model, a restricted case of the ABC flow model, and so on, are shown to be integrable in the above sense.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.14242",
  "author_total": 1,
  "authors": [
    {
      "name": "Shin-itiro Goto"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5k8gz3k1fbd1g.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.14242",
  "fulltext_url": null,
  "id": "5k8gz3k1fbd1g",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.14242",
  "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"
    ],
    [
      "openalex",
      "3103|Advanced Differential Geometry Research"
    ]
  ],
  "openalex": "W7213343301",
  "pdf_url": "https://arxiv.org/pdf/2609.14242",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-13",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5k8gz3k1fbd1g.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:21:25Z",
      "native_id": "2609.14242",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.14242"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Liouville integrability of Beltrami-Maxwell fields with sources: A geometric theory of magnetic surfaces",
  "title_text": "Liouville integrability of Beltrami-Maxwell fields with sources: A geometric theory of magnetic surfaces",
  "type": "preprint",
  "updated_at": "2026-10-30T12:21:29Z",
  "url": "https://research.draconitic.com/paper/5k8gz3k1fbd1g",
  "venue": "arXiv",
  "versions": []
}