从非对易几何重新思考Connes对粒子物理标准模型的研究
Rethinking Connes' approach to the standard model of particle physics via non-commutative geometry
摘要：
康纳斯的非对易几何（NCG）是黎曼几何的推广，特别适合于表达与爱因斯坦引力耦合的粒子物理学的标准模型。在以前的论文中，我们提出了这个框架的重新表述：（i）更简单，更统一的公理，和（ii）允许拉格朗日粒子物理学的标准模型（耦合到爱因斯坦引力）的方式来指定更紧密，更解释性比传统的算法的基础上有效场论。在这里，我们解释如何相同的重新制定产生一个新的角度对一个给定的NCG的对称性。把这个观点应用到传统上用来描述标准模型的NCG中，我们发现，相反，标准模型的一个扩展是额外的$U(1)_{B-L}$规范对称性，以及一个额外的复数标量场$σ$，它是$SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$下的单线态，但具有$B-L=2$。这个领域具有宇宙学意义，并为观测到的希格斯质量与NCG预测之间的差异提供了新的解决方案。
英文摘要：
Connes' non-commutative geometry (NCG) is a generalization of Riemannian geometry that is particularly apt for expressing the standard model of particle physics coupled to Einstein gravity. In a previous paper, we suggested a reformulation of this framework that is: (i) simpler and more unified in its axioms, and (ii) allows the Lagrangian for the standard model of particle physics (coupled to Einstein gravity) to be specified in a way that is tighter and more explanatory than the traditional algorithm based on effective field theory. Here we explain how this same reformulation yields a new perspective on the symmetries of a given NCG. Applying this perspective to the NCG traditionally used to describe the standard model we find, instead, an extension of the standard model by an extra $U(1)_{B-L}$ gauge symmetry, and a single extra complex scalar field $σ$, which is a singlet under $SU(3)_{C}\times SU(2)_{L}\times U(1)_{Y}$, but has $B-L=2$. This field has cosmological implications, and offers a new solution to the discrepancy between the observed Higgs mass and the NCG prediction.
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。
