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A topological model of composite preons from the minimal ideals of two Clifford algebras
Physics Letters B ( IF 4.4 ) Pub Date : 2020-09-01 , DOI: 10.1016/j.physletb.2020.135687
Niels G. Gresnigt

Abstract This paper demonstrates a direct correspondence between a recent algebraic characterization of leptons and quarks as basis elements of the minimal one-sided ideals of the complex Clifford algebras C l ( 6 ) and C l ( 4 ) , shown earlier to transform as a single generation of leptons and quarks under the Standard Model's unbroken S U ( 3 ) c × U ( 1 ) e m and S U ( 2 ) L gauge symmetries respectively, and a topological formulation of the Harari-Shupe preon model in which leptons and quarks are represented in terms of braids. It was previously shown that mapping a Witt basis of C l ( 6 ) to particular braids in the circular Artin braid group B 3 c makes it possible to replicate the topological structure describing electrocolor symmetries in this preon model. This paper extends this curious correspondence, which involves only the minimal ideals of C l ( 6 ) under S U ( 3 ) c × U ( 1 ) e m , to include the S U ( 2 ) L chiral weak symmetry. This is achieved by mapping a Witt basis of an additional C l ( 4 ) algebra to braids in B 3 , taken to be a subgroup of B 3 c . The braids corresponding to the charged vector bosons are determined, and it is demonstrated that chiral weak interactions can be described via the composition of braids.

中文翻译:

来自两个 Clifford 代数的极小理想的复合前子拓扑模型

摘要 本文证明了轻子和夸克作为复数克利福德代数 C l ( 6 ) 和 C l ( 4 ) 的最小单边理想的基本元素的最近代数表征之间的直接对应关系,前面显示为单个变换。分别在标准模型的完整 SU ( 3 ) c × U ( 1 ) em 和 SU ( 2 ) L 规范对称性下产生轻子和夸克,以及 Harari-Shupe 前子模型的拓扑公式,其中轻子和夸克表示在辫子的术语。先前已经表明,将 C l (6) 的 Witt 基映射到圆形 Artin 编织组 B 3 c 中的特定编织,可以复制描述此 preon 模型中电色对称性的拓扑结构。这篇论文扩展了这种奇怪的通信,它只涉及 SU (3) c × U ( 1 ) em 下 C l ( 6 ) 的极小理想,以包括 SU ( 2 ) L 手征弱对称性。这是通过将附加 C l (4) 代数的 Witt 基映射到 B 3 中的辫子来实现的,B 3 被视为 B 3 c 的子群。确定了对应于带电矢量玻色子的辫子,并证明了手性弱相互作用可以通过辫子的组成来描述。
更新日期:2020-09-01
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