论文标题
来自两个Clifford代数的最低理想的复合预装的拓扑模型
A topological model of composite preons from the minimal ideals of two Clifford algebras
论文作者
论文摘要
我们演示了复杂Clifford代数$ \ Mathbb {C} \ ell（6）$和$ \ Mathbb {C} \ Ell（4）$的基本理想的基本状态之间的直接对应关系，前面显示为在标准模型的leptons and Quarks和Quarks中转变为标准模型的Unbroken of Brount $ su（$ su）和Quarks。 $ su（2）_l $ gauge对称性，以及一个基于拓扑的玩具模型，其中leptons，Quarks和Gauge Bosons表示为编织组$ B_3 $的元素。 先前的表明，映射$ \ mathbb {c} \ ell（6）$的最小左左左左左原理的基础状态，以精确地在现有的拓扑preogical preon模型中精确地复制了描述电气上对称性的简单拓扑结构。本文通过包括$ \ mathbb {c} \ ell（4）$代数来扩展这些结果以结合手性弱对称性，并确定具有简单辫子的最小正确理想的基础状态。确定了与带电向量玻色子相对应的辫子，并证明可以通过编织的组成来描述弱相互作用。
We demonstrate a direct correspondence between the basis states of the minimal ideals of the complex Clifford algebras $\mathbb{C}\ell(6)$ and $\mathbb{C}\ell(4)$, shown earlier to transform as a single generation of leptons and quarks under the Standard Model's unbroken $SU(3)_c\times U(1)_{em}$ and $SU(2)_L$ gauge symmetries respectively, and a simple topologically-based toy model in which leptons, quarks, and gauge bosons are represented as elements of the braid group $B_3$. It was previously shown that mapping the basis states of the minimal left ideals of $\mathbb{C}\ell(6)$ to specific braids replicates precisely the simple topological structure describing electrocolor symmetries in an existing topological preon model. This paper extends these results to incorporate the chiral weak symmetry by including a $\mathbb{C}\ell(4)$ algebra, and identifying the basis states of the minimal right ideals with simple braids. The braids corresponding to the charged vector bosons are determined, and it is demonstrated that weak interactions can be described via the composition of braids.
