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An Algebraic Roadmap of Particle Theories, Part I: General construction
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abstract
Expanding the results of [1], [2], [3], we demonstrate a network of algebraic connections between six well-known particle theories. These are the Spin(10) model, the Georgi-Glashow model, the Pati-Salam model, the Left-Right Symmetric model, the Standard Model both pre- and post-Higgs mechanism. A new inclusion of a quaternionic reflection within the network further differentiates $W^{\pm}$ bosons from the $Z^0$ boson in comparison to the Standard Model. It may introduce subtle new considerations for the phenomenology of electroweak symmetry breaking.
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Standard Model Symmetries and the Nested Embeddings of $\mathbb{R}\subset\mathbb{C}\subset\mathbb{H}\subset\mathbb{O}$
The Standard Model gauge group and its charge operators emerge from O⊕H⊕C⊕R by stabilizing top-graded elements and imposing an equal-trace condition.
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