{
  "abstract": "A symmetric representation of Minkowski spacetime is constructed by combining a normalized fourth-order Hadamard transformation with an imaginary temporal coordinate. The resulting complex coordinates $q^a$ distribute time and space equally among four components and transform the Minkowski metric into a Euclidean-form complex bilinear metric. The four Hadamard spatial sign vectors form a regular tetrahedron and appear simultaneously in the transformed Dirac and Maxwell operators. The Dirac matrices satisfy a Euclidean-form Clifford algebra and contain tetrahedral combinations of Pauli matrices, whereas the Riemann--Silberstein Maxwell matrices realize the corresponding spin-1 structure. A gauge-invariant QED Lagrangian is formulated in the same coordinates. In Fourier space, the Dirac and Maxwell systems are governed by the common invariant $κ_aκ^a$, while the complete Maxwell operator admits an exact rectangular Clifford-like factorization. The formulation is further extended to the weak-field Einstein--Dirac--Maxwell system. In harmonic gauge, the linearized gravitational field is governed by the same scalar wave operator $\\Box_q$, while gravitational corrections to the Dirac and Maxwell equations enter through the perturbed tetrad, spin connection, and curvature. This common principal-operator structure suggests shared spectral kernels and scalar-wave preconditioning for coupled field solvers.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.09617",
  "author_total": 1,
  "authors": [
    {
      "name": "Farhad Aghili"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/750fz3b1exp09.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09617",
  "fulltext_url": null,
  "id": "750fz3b1exp09",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09617",
  "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",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7212169621",
  "pdf_url": "https://arxiv.org/pdf/2609.09617",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-09",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/750fz3b1exp09.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09617",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09617"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Hadamard--Tetrahedral Symmetric Spacetime and Clifford-Like Factorizations of Dirac and Maxwell Operators",
  "title_text": "Hadamard--Tetrahedral Symmetric Spacetime and Clifford-Like Factorizations of Dirac and Maxwell Operators",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/750fz3b1exp09",
  "venue": "arXiv",
  "versions": []
}