{
  "abstract": "We present the explicit theory of the Joss-Weinberg covariant field with spin $\\frac{3}{2}$ which is a eight-dimensional massive covariant field transforming according to the representation $(\\frac{3}{2},0)\\oplus(0, \\frac{3}{2})$ of the group $SL(2,\\mathbb{C})$. As the transformation matrices of this representation are still unknown, we apply a new method for deriving them using exclusively maximally reducible representations, e. g. $(1,0)\\otimes(\\frac{1}{2},0)$ instead of the irreducible one $(1,\\frac{1}{2})=(1,0)\\otimes(0,\\frac{1}{2})$ we meet in usual frameworks. After applying this method, we obtain a $12$-component covariant field transforming according to the representation $[(1,0)\\otimes(\\frac{1}{2},0)]\\oplus [(0,1)\\otimes(0, \\frac{1}{2})]$ which is maximally reducible, up to subspaces of irreducible representations of the $SU(2)$ group. Consequently, after developing the theory in the direct product basis of the representation $(1,0)\\otimes(\\frac{1}{2},0)$, we can separate the sector of spin half revealing thus the genuine Joss-Weinberg covariant field of spin $\\frac{3}{2}$, transforming according to the representation $(\\frac{3}{2},0)\\oplus(0, \\frac{3}{2})$. In this manner the theory of Joss-Weinberg covariant field of spin $\\frac{3}{2}$ can be build naturally deriving the field equation and associated matrices, Lagrangian formalism, inner product and the closed expressions of the orthonormal mode spinors.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2605.28877",
  "author_total": 1,
  "authors": [
    {
      "name": "Ion I. Cotaescu"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6a8m116zb9sh4.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2605.28877",
  "fulltext_url": null,
  "id": "6a8m116zb9sh4",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2605.28877",
  "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",
      "physics.gen-ph"
    ],
    [
      "openalex",
      "3106|Black Holes and Theoretical Physics"
    ]
  ],
  "openalex": "W7162786406",
  "pdf_url": "https://arxiv.org/pdf/2605.28877",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6a8m116zb9sh4.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2605.28877",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2605.28877"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Black Holes and Theoretical Physics",
      "subfield": "high-energy"
    }
  ],
  "title": "Joss-Weinberg covariant field with mass and spin $\\frac{3}{2}$",
  "title_text": "Joss-Weinberg covariant field with mass and spin 3/2",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/6a8m116zb9sh4",
  "venue": "arXiv",
  "versions": []
}