What question did this study set out to answer?

This research aims to derive the Dirac equation from octonionic structures and unify Standard Model fermions.

June 8, 2026Open Access

Paper XIV: The Octonionic Dirac Equation

Key Points

This research aims to derive the Dirac equation from octonionic structures and unify Standard Model fermions.
Derivation of the Dirac equation from the octonionic brane-bulk framework.
Identification of Dirac gamma matrices with elements of H+.
Exploration of CPT symmetry and its relationship with H+ and H−.
Dirac equation is successfully described using octonionic structures.
Antimatter is represented through H− with corresponding relationships to H+.
All Standard Model fermions can be viewed as modes of the same octonionic wave equation.

Abstract

The Dirac equation is derived from the octonionic brane-bulk structure as the equation of motion for a focal deceleration zone propagating through the expanding brane. The four Dirac gamma matrices γ0, γ1, γ2, γ3 are identied with the four ele- ments of H+ = 1, e1, e2, e3: γ0 corresponds to the real unit (temporal evolution), γ1, γ2, γ3 to the three imaginary units e1, e2, e3 (spatial momentum). The Dirac algebra γm, γn = 2ηmn follows from the quaternionic multiplication relations in H+. Antimatter (positrons) corresponds to the H−representation, as derived in Paper VII. CPT symme- try is the simultaneous interchange H+ ↔H−, time-reversal (the real unit of H+), and spatial parity (the three imaginary units of H+). The octonionic Dirac equation unies all Standard Model fermions as dierent modes of the same octonionic wave equation. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10. 5281/zenodo. 19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M. D. , University of Minnesota. ORCID: 0000-0002-1143-941X.

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