标题： 非阿贝尔Weyl对称性 显示英文标题

标题： Non-Abelian Weyl Symmetry

摘要： 由赫尔曼·外尔提出的阿贝尔规范对称性被推广到其非阿贝尔扩展。 随后，标准模型被推广以包含阿贝尔和非阿贝尔的外尔对称性。 这种对称性的扩展引入了新的规范粒子，这些粒子可以作为暗物质的潜在候选者。 它还自然地将第二个标量场引入理论中。 外尔对称性的破缺使这个标量场成为了一个维度常数，使得希格斯粒子成为标准模型中的唯一标量成分。 除了预期的好处之外，还有三个意外的额外收获：(1) 它带来了一些关于宇称破坏的新理解；(2) 它为希格斯机制中的符号问题提供了一个答案；(3) 它为中微子的本质提供了一些新的视角：非阿贝尔外尔对称性要求存在\textit{必须是}个右手性中微子；此外，中微子质量的微小性由非阿贝尔外尔对称性保护。 显示英文摘要

摘要： The Abelian gauge symmetry proposed by Hermann Weyl is generalized to its non-Abelian extension. Afterwards the standard model is generalized to incorporate the Abelian and non-Abelian Weyl symmetry. This symmetry extension brings new gauge particles that can be potential candidates for the dark matter. It also naturally introduces a second scalar field into the theory. The breaking of the Weyl symmetry turns this scalar field into a dimensional constant, making the Higgs as the only scalar component in the standard model. In addition to the expected benefits, there are three unexpected bonuses: (1) it brings some new understanding of the parity violation; (2) it provides an answer to the sign problem in the Higgs mechanism; (3) it gives some new perspectives on the nature of the neutrino: non-Abelian Weyl symmetry demands that there \textit{must be} right-handed netrino; furthermore, the smallness of the neutrino mass is protected by the non-Abelian Weyl symmetry.