{
  "abstract": "We propose a reformulation of the Feynman propagator in terms of the tessarine algebra, in which the vacuum is represented as a stationary condensate of hyperbolic rapidities rather than as a transient ensemble of virtual particles. The construction begins by expressing the momentum-space measure d³p in rapidity coordinates and identifying the atemporal, isotropic section of the tessarine wave function Ψ(0, β) = 2 cosh β as the natural vacuum amplitude. The resulting integral reproduces the standard vacuum energy density ρᵥ while revealing a quartic exponential divergence ∼ ∫ e⁴ᵝ dβ. We introduce a physically motivated rapidity cutoff yₘₐₓ ≈ 1.93, constrained by the observed upper bound on cosmological recession velocity and the lightest neutrino mass scale, and show that this cutoff may offer a new perspective on the vacuum energy discrepancy. We further observe that the Planck frequency arises as the geometric mean of the Schwarzschild frequency and the Margolus–Levitin computational bound, a relation that follows directly from the conformal inversion r ↦ 1/r underlying the tessarine framework. This inversion is interpreted as a geometric barrier analogous to confinement in gauge theories. Throughout, we distinguish carefully between identities inherited from established physics and the interpretive extensions proposed here.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Rodrigo Silva Barros"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/8rz50vmabmaap.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23420233",
  "fulltext_url": null,
  "id": "8rz50vmabmaap",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23420233",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
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  "pdf_url": "https://zenodo.org/api/records/23420233/files/A%20Tessarine%20Reformulation%20of%20the%20Feynman%20Propagator.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/8rz50vmabmaap.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:41Z",
      "native_id": "23420233",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23420233"
    }
  ],
  "subjects": [],
  "title": "A Tessarine Reformulation of the Feynman Propagator: Rapidity Cutoff, Vacuum Condensate, and the Planck Frequency as a Geometric Mean",
  "title_text": "A Tessarine Reformulation of the Feynman Propagator: Rapidity Cutoff, Vacuum Condensate, and the Planck Frequency as a Geometric Mean",
  "type": "preprint",
  "updated_at": "2026-10-30T12:33:39Z",
  "url": "https://research.draconitic.com/paper/8rz50vmabmaap",
  "venue": "Zenodo",
  "versions": []
}