标准模型代数-从复克利福德代数Cl6看轻子、夸克和规范
The Standard Model Algebra - Leptons, Quarks, and Gauge from the Complex Clifford Algebra Cl6
摘要：
一个简单的几何代数自动包含一个家庭的标准模型的轻子和夸克，和电弱和色规范对称性，没有预测额外的粒子和对称。该代数已经自然地存在于标准模型中，在克利福德代数$\mathbb{C}\ell_6$的两个实例中，一个是由狄拉克代数和弱对称生成元代数生成的，另一个是由色对称的复杂三维表示生成的，它生成维特分解，导致代数分解为代表轻子和夸克的理想。这两个实例是同构的，最小的方法是识别它们，从而产生这里提出的模型。狄拉克代数和洛伦兹代数自然地表现为作用于代表轻子和夸克的理想的子代数。由此产生的理想上的表示是不变的电磁和颜色的对称性，这是由代数的双向量产生的。电弱对称性也存在，而且它已经被代数的几何打破了。该模型预测由$\sin^2θ_W=0.25$给出的裸温伯格角$θ_W$。该模型与以前已知的模型有共同的想法，特别是Chisholm和Farwell，1996，Trayling和Baylis，2004，以及Furey，2016。
英文摘要：
A simple geometric algebra is shown to contain automatically the leptons and quarks of a family of the Standard Model, and the electroweak and color gauge symmetries, without predicting extra particles and symmetries. The algebra is already naturally present in the Standard Model, in two instances of the Clifford algebra $\mathbb{C}\ell_6$, one being algebraically generated by the Dirac algebra and the weak symmetry generators, and the other by a complex three-dimensional representation of the color symmetry, which generates a Witt decomposition which leads to the decomposition of the algebra into ideals representing leptons and quarks. The two instances being isomorphic, the minimal approach is to identify them, resulting in the model proposed here. The Dirac and Lorentz algebras appear naturally as subalgebras acting on the ideals representing leptons and quarks. The resulting representations on the ideals are invariant to the electromagnetic and color symmetries, which are generated by the bivectors of the algebra. The electroweak symmetry is also present, and it is already broken by the geometry of the algebra. The model predicts a bare Weinberg angle $θ_W$ given by $\sin^2θ_W=0.25$. The model shares common ideas with previously known models, particularly with Chisholm and Farwell, 1996, Trayling and Baylis, 2004, and Furey, 2016.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
