An Algebraic Roadmap of Particle Theories

IF 2.2 4区物理与天体物理 Q2 PHYSICS, MULTIDISCIPLINARY

Annalen der Physik Pub Date : 2025-02-16 DOI:10.1002/andp.202400324

Nichol Furey

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Abstract

In this study, the detailed symmetry breaking pathways established in Furey et al. (2024) are bypassed. Instead, a direct route from the Spin(10) model to the Standard Model is enabled via a single algebraic constraint.

This single constraint, however, may be reconfigured as a requirement that three $so (10)$ actions coincide on a fixed space of multi-vector fermions. This $so (10) \mapsto su {(3)}_{C} \oplus su {(2)}_{L} \oplus u {(1)}_{Y}$ breaking (from a three-way intersection) mirrors, in certain ways, the $so (8) \mapsto g_{2}$ breaking (from a three-way intersection) in the context of octonionic triality. By extending this result to include quaternions and complex numbers, we find that a five-way intersection breaks $so (10) \mapsto su {(3)}_{C} \oplus u {(1)}_{Q}$ . These are the Standard Model's unbroken gauge symmetries, post-Higgs-mechanism.

Abstract Image

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粒子理论的代数路线图

在本研究中，我们绕过了Furey等人（2024）建立的详细的对称性破缺路径。相反，从Spin（10）模型到标准模型的直接路由是通过单个代数约束实现的。然而，这个单一的约束可以被重新配置为三个so (10)$ \mathfrak {so}(10)$动作在多向量费米子的固定空间上重合的要求。这就是(10)∑su (3) C⊕su (2) L⊕u (1) Y $\mathfrak{so}(10)\hspace{1.42262pt}\mapsto \hspace{1.42262pt}\mathfrak {su}(3)_{\textup {C}}\oplus \mathfrak {su}(2)_{\textup {L}}\oplus \mathfrak {u}(1)_{\textup {Y}}$ break（从三路交叉口）在某些方面是镜像的，so(8)∑2 $\mathfrak {so}(8)\hspace{1.42262pt}\mapsto \hspace{1.42262pt}\ mathfrak {g}_{2}$ break(从一个三向交叉)在八元性的背景下。通过将这个结果扩展到四元数和复数，我们发现了一个五路交叉口的断点so(10)∑su (3) C⊕u (1) Q $\mathfrak {so}(10)\hspace{1.42262pt}\mapsto \hspace{1.42262pt}\mathfrak {su}(3)_{\textup {C}}\oplus \mathfrak {u}(1)_{\textup {Q}}$。这就是标准模型的未破缺规范对称性，即后希格斯机制。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Annalen der Physik 物理-物理：综合

CiteScore

4.50

自引率

8.30%

发文量

202

审稿时长

3 months

期刊介绍： Annalen der Physik (AdP) is one of the world''s most renowned physics journals with an over 225 years'' tradition of excellence. Based on the fame of seminal papers by Einstein, Planck and many others, the journal is now tuned towards today''s most exciting findings including the annual Nobel Lectures. AdP comprises all areas of physics, with particular emphasis on important, significant and highly relevant results. Topics range from fundamental research to forefront applications including dynamic and interdisciplinary fields. The journal covers theory, simulation and experiment, e.g., but not exclusively, in condensed matter, quantum physics, photonics, materials physics, high energy, gravitation and astrophysics. It welcomes Rapid Research Letters, Original Papers, Review and Feature Articles.