{
  "abstract": "We extend the interpolation of the Poincaré algebra between instant form dynamics (IFD) and light-front dynamics (LFD) to the conformal algebra in $(3+1)$ dimensions. Building upon our recent formulation of the interpolating conformal algebra in $(1+1)$ dimensions, we propose an interpolation method for the conformal group $SO(4,2)$. A central feature of this work is classifying the $15$ conformal generators into kinematic and dynamic categories as a function of the interpolation angle ($0 \\leq δ\\leq \\fracπ{4}$). We show that among the five additional generators beyond the Poincaré group, the dilatation generator remains strictly kinematic across the entire interpolation region. We also find that in the exact light-front limit ($δ= \\fracπ{4}$), one additional generator from the Special Conformal Transformations (SCT) becomes kinematic in $(1+1)$ but dynamical in $(3+1)$. This behavior shows the advantage of LFD in maximizing kinematic generators and minimizing dynamical complexity. To support this algebraic framework, we construct a $6 \\times 6$ interpolating projective spacetime matrix representation. We detail the explicit transformations of the interpolating time under all $15$ generators, providing a systematic view of conformal symmetry across the relativistic dynamics.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.36297",
  "author_total": 2,
  "authors": [
    {
      "name": "Hariprashad Ravikumar"
    },
    {
      "name": "Chueng-Ryong Ji"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bre0swcxf2jqr.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.36297",
  "fulltext_url": null,
  "id": "bre0swcxf2jqr",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.36297",
  "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",
      "hep-ph"
    ],
    [
      "arxiv",
      "hep-th"
    ],
    [
      "openalex",
      "3103|Relativity and Gravitational Theory"
    ]
  ],
  "openalex": "W7214939913",
  "pdf_url": "https://arxiv.org/pdf/2609.36297",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-28",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bre0swcxf2jqr.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2609.36297",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.36297"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:hep-ph",
      "subfield": "high-energy"
    }
  ],
  "title": "Interpolating conformal algebra in $(3+1)$ dimensions between the instant form and the light-front form of relativistic dynamics",
  "title_text": "Interpolating conformal algebra in (3+1) dimensions between the instant form and the light-front form of relativistic dynamics",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/bre0swcxf2jqr",
  "venue": "arXiv",
  "versions": []
}