{
  "paper_id": "qqc-000-quaternionic-wavefunction",
  "title": "The Quaternionic Wavefunction: Spin-1/2 Particles, S^3, and SU(2)",
  "slug": "quaternionic-wavefunction",
  "version": "0.1.0",
  "status": "draft",
  "publication_date": null,
  "last_updated": "2026-04-10",
  "authors": [
    {
      "name": "John G. Van Geem",
      "affiliation": "RQM Technologies",
      "orcid": "0009-0002-4003-8452",
      "email": null,
      "corresponding": true
    }
  ],
  "abstract": "This paper introduces the quaternionic wavefunction as a compact way to organize the standard spinor geometry of a spin-1/2 particle. Starting from a normalized two-component complex state vector $\\left(\\alpha,\\beta\\right)$ in $\\mathbb{C}^2$, it groups the four real coefficients into a single quaternion $q_{\\psi}=a_0+a_1 i+b_0 j+b_1 k$. Under this identification, normalization becomes $\\lvert q_{\\psi}\\rvert=1$, so the space of normalized representatives is the three-sphere $S^3$. The paper then distinguishes carefully between two roles played by the same manifold: $S^3$ as the state-representative sphere of normalized spinors, and $S^3$ as the manifold underlying the Lie group of unit quaternions, which models $\\mathrm{SU}(2)$. This makes the geometry of spin-1/2 particles more transparent: the quaternionic wavefunction transforms naturally under $\\mathrm{SU}(2)$, and the double cover $\\mathrm{SU}(2)\\to\\mathrm{SO}(3)$ explains why $2\\pi$ and $4\\pi$ rotations behave differently for spinors. The mathematical content is standard; the project-specific contribution is the expository framing. The paper does not propose a new physical theory and does not claim quaternionic Hilbert-space quantum mechanics beyond this geometric re-expression of ordinary spin-1/2 structure.",
  "keywords": [
    "quaternionic wavefunction",
    "spin-1/2",
    "spinors",
    "S^3",
    "SU(2)",
    "unit quaternions"
  ],
  "series": "RQM Quaternionic Quantum Computing Prelude",
  "series_number": 1,
  "depends_on": [],
  "canonical_url": null,
  "pdf_url": null,
  "html_url": null,
  "jats_url": null,
  "doi": null,
  "journal": null,
  "volume": null,
  "issue": null,
  "pages": null,
  "citations": [
    "adler1995",
    "hall2015",
    "kuipers1999",
    "nielsen2010",
    "penrose1984"
  ],
  "related_artifacts": [
    "main.tex",
    "artifacts/code/README.md"
  ],
  "license": "CC-BY-4.0",
  "notes": "Conceptual prequel paper introducing the quaternionic wavefunction as the grouping of a two-component complex spinor into one quaternion. Intended to precede qqc-001-foundations conceptually without making new-physics claims.",
  "domain": "quantum_computing"
}