An Algebraic Roadmap of Particle Theories, Part I: General construction

TL;DR

This paper constructs an algebraic framework connecting six major particle theories, revealing new insights into electroweak symmetry breaking and differentiating key bosons through quaternionic reflections.

Contribution

It introduces a novel algebraic network linking six particle theories and incorporates quaternionic reflections to distinguish bosons, advancing theoretical understanding.

Findings

Established algebraic connections between six particle theories

Identified quaternionic reflection as a differentiator for W and Z bosons

Potential implications for electroweak symmetry breaking phenomenology

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.