What does this research mean for the field?

The Dirac equation and all Standard Model fermions can be unified and derived from an octonionic brane-bulk structure, with Dirac gamma matrices corresponding to elements of a quaternionic sub-algebra. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This work derives the Dirac equation from an octonionic brane-bulk structure, exploring novel implications for particle physics.

May 22, 2026Open Access

Paper XIV of the Brane-Bulk Series The Octonionic Dirac Equation B. D. Jagadeesan, MD

Key Points

This work derives the Dirac equation from an octonionic brane-bulk structure, exploring novel implications for particle physics.
Derived the Dirac equation using octonionic brane-bulk structures.
Identified Dirac gamma matrices with elements of the set H+ for temporal and spatial components.
Discussed implications of CPT symmetry and antifermions in the context of octonionic representations.
Established that the Dirac equation can represent all Standard Model fermions as modes of one octonionic wave equation.
Highlighted the significance of quaternionic multiplication in deriving the Dirac algebra.
Demonstrated a framework for understanding antimatter through the H- representation.

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.

Paper XIV of the Brane-Bulk Series The Octonionic Dirac Equation B. D. Jagadeesan, MD

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