{
  "abstract": "We show how genuine three-body phase information can enter the invariant mass of a relativistic three-particle Dirac system in $(1+1)$ dimensions. As a solvable reference system, we consider the Sakamoto--Munakata--Ino model with pairwise contact interactions $g_{ij}(1-α_iα_j)δ(x_i-x_j)$. These singular interactions can be transferred into sector-dependent phases and matching conditions by a discontinuous unitary transformation. Although the explicit contact terms are thereby removed, the nonzero constituent-mass operator is rotated and retains nontrivial spectral information. We introduce a genuine three-body holonomy generated by $Q_3=α_1α_2α_3$. The kinetic and pair-interaction parts commute with $Q_3$, while the constituent-mass operator anticommutes with it. Consequently, the massless system separates into the $Q_3=\\pm1$ sectors, which acquire opposite holonomy phases $e^{\\pm iθ_3}$, whereas nonzero constituent masses mix the two sectors. This phase-sector-mixing mechanism makes the relative three-body phase dynamically accessible to the bound-state spectrum and establishes an operator-level mechanism through which the three-body holonomy generates a $θ_3$ dependence of the physical three-body invariant mass. We further emphasize that the topological three-body holonomy is not automatically equivalent to a bare triple-contact potential; such an equivalence requires a regulated self-adjoint realization and a compatible interaction-dependent boost satisfying the Poincaré algebra. The resulting framework therefore connects genuine three-body phase information to the mass spectrum of a relativistic composite system while clearly separating the controlled holonomy construction from the unresolved short-distance triple-contact realization.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.25478",
  "author_total": 1,
  "authors": [
    {
      "name": "Tadashi Yoshikawa"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/0ebase6z06f54.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.25478",
  "fulltext_url": null,
  "id": "0ebase6z06f54",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.25478",
  "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",
      "physics.gen-ph"
    ],
    [
      "openalex",
      "2610|Spectral Theory in Mathematical Physics"
    ]
  ],
  "openalex": "W7214090081",
  "pdf_url": "https://arxiv.org/pdf/2609.25478",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0ebase6z06f54.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:39Z",
      "native_id": "2609.25478",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.25478"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2610|Spectral Theory in Mathematical Physics",
      "subfield": "mathematical-physics"
    }
  ],
  "title": "Phase Encoding of Genuine Three-Body Interactions in a Relativistic Dirac System in $1+1$ Dimensions",
  "title_text": "Phase Encoding of Genuine Three-Body Interactions in a Relativistic Dirac System in 1+1 Dimensions",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:39Z",
  "url": "https://research.draconitic.com/paper/0ebase6z06f54",
  "venue": "arXiv",
  "versions": []
}