Division Algebras and the Standard Model Gauge Group

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Main Author: Novickis, Alexander
Format: Recurso digital
Published: Zenodo 2026
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contents <p><strong>Title:</strong> Division Algebras and the Standard Model Gauge Group</p> <p><strong>Author:</strong> Alexander Novickis (alex.novickis@gmail.com)</p> <p>The Standard Model gauge group $SU(3)_c \times SU(2)_L \times U(1)_Y$ is one of the most precisely tested structures in physics, yet its origin remains unexplained within conventional quantum field theory. We show that this gauge group emerges inevitably from the algebraic and topological structure of the four normed division algebras $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{O}$ together with the Hopf fibration chain. Hurwitz's theorem (1898) guarantees that exactly four normed division algebras exist; the automorphism groups of these algebras contain precisely $U(1)$, $SU(2)$, and $SU(3)$ as gauge symmetries. Within the topological soliton framework, these abstract algebraic facts are physically realized through Kaluza-Klein reduction on the internal space $S^3 \times S^7$ (Paper X): the $S^3$ fiber gives $SU(2)$, the $S^7$ structure gives $SU(3)$ via $G_2 \supset SU(3)$, and the Hopf $S^1$ within $S^3 \to S^2$ gives $U(1)$. No grand unified group is needed, no symmetry breaking from a larger group is required, and charge quantization follows from the division algebra constraint rather than from $SU(5)$ embedding. The framework predicts absolute proton stability, no new gauge bosons beyond the Standard Model, and no leptoquarks — all consistent with current experimental bounds.</p> <p><strong>Keywords:</strong> physics, topology, soliton, algebra, gauge theory, division algebras</p> <p><strong>DOI:</strong> <a href="https://doi.org/10.5281/zenodo.19349095">10.5281/zenodo.19349095</a></p> <p><strong>Series:</strong> Paper LIV in the Hopf Soliton Programme</p>
format Recurso digital
id zenodo_https___doi_org_10_5281_zenodo_19590311
institution Zenodo
language
publishDate 2026
publisher Zenodo
record_format zenodo
spellingShingle Division Algebras and the Standard Model Gauge Group
Novickis, Alexander
physics
topology
soliton
algebra
gauge-theory
division-algebras
<p><strong>Title:</strong> Division Algebras and the Standard Model Gauge Group</p> <p><strong>Author:</strong> Alexander Novickis (alex.novickis@gmail.com)</p> <p>The Standard Model gauge group $SU(3)_c \times SU(2)_L \times U(1)_Y$ is one of the most precisely tested structures in physics, yet its origin remains unexplained within conventional quantum field theory. We show that this gauge group emerges inevitably from the algebraic and topological structure of the four normed division algebras $\mathbb{R}$, $\mathbb{C}$, $\mathbb{H}$, $\mathbb{O}$ together with the Hopf fibration chain. Hurwitz's theorem (1898) guarantees that exactly four normed division algebras exist; the automorphism groups of these algebras contain precisely $U(1)$, $SU(2)$, and $SU(3)$ as gauge symmetries. Within the topological soliton framework, these abstract algebraic facts are physically realized through Kaluza-Klein reduction on the internal space $S^3 \times S^7$ (Paper X): the $S^3$ fiber gives $SU(2)$, the $S^7$ structure gives $SU(3)$ via $G_2 \supset SU(3)$, and the Hopf $S^1$ within $S^3 \to S^2$ gives $U(1)$. No grand unified group is needed, no symmetry breaking from a larger group is required, and charge quantization follows from the division algebra constraint rather than from $SU(5)$ embedding. The framework predicts absolute proton stability, no new gauge bosons beyond the Standard Model, and no leptoquarks — all consistent with current experimental bounds.</p> <p><strong>Keywords:</strong> physics, topology, soliton, algebra, gauge theory, division algebras</p> <p><strong>DOI:</strong> <a href="https://doi.org/10.5281/zenodo.19349095">10.5281/zenodo.19349095</a></p> <p><strong>Series:</strong> Paper LIV in the Hopf Soliton Programme</p>
title Division Algebras and the Standard Model Gauge Group
topic physics
topology
soliton
algebra
gauge-theory
division-algebras
url https://doi.org/10.5281/zenodo.19590311