A Tessarine Reformulation of the Feynman Propagator: Rapidity Cutoff, Vacuum Condensate, and the Planck Frequency as a Geometric Mean
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.
Related
- Conformal Rapidity and the Tessarine Engine: Exponential Radial Inversion and the Internal Structure of Black Holes
- Harmonic-Field Duality: 132Hz as the Geometric Frequency Quantum of E8 — E8 Intelligence Research
- Relativistic Mass Transport and Geometric Coupling: High-Frequency 2¹⁵ Hz Quartz Reflection for Volumetric Light-Speed Displacement
- Enhancing magnonic frequency combs via geometric nonlinearity
- An Application of Geometric Riemannian Pricing Algorithm for Valuing Catastrophe Bonds in Incomplete Markets: Market-Consistent Financial Entropy and the Split of Frequency and Severity Risk Premia
BibTeX
@misc{barros2026tessarine,
title = {{A Tessarine Reformulation of the Feynman Propagator: Rapidity Cutoff, Vacuum Condensate, and the Planck Frequency as a Geometric Mean}},
author = {Rodrigo Silva Barros},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23420233},
url = {https://zenodo.org/records/23420233},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - A Tessarine Reformulation of the Feynman Propagator: Rapidity Cutoff, Vacuum Condensate, and the Planck Frequency as a Geometric Mean
AU - Rodrigo Silva Barros
PY - 2026
DA - 2026/10/16
PB - Zenodo
DO - 10.5281/zenodo.23420233
UR - https://zenodo.org/records/23420233
AB - 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.
ER -