论文标题
重力自旋连接的纯仪表理论
Pure gauge theory for the gravitational spin connection
论文作者
论文摘要
重力自旋连接在重力中以非压缩的Lorentz Group $ SO（3,1）$的非亚洲仪表场出现。一般相对性的作用是与自旋连接相关的场强中的线性，其运动方程对应于标准的度量约束。因此，零反应旋转连接永远不会被实现为独立的自由度，并且由维尔贝因场决定。在这项工作中，我们采用不同的观点，并考虑了纯阳米尔斯理论，用于旋转连接与Dirac Fermions相连，从而导致前者是一个动力学领域。在讨论了管理与非紧密量规理论相关的病理学的各种方法之后，我们通过自旋连接交换来计算养树级振幅用于费米昂散射。与在Fermions存在的情况下整合扭转相反，该模型会诱导手性的四效项，涉及右前电流相互作用，该术语不存在于标准模型中。
The gravitational spin connection appears in gravity as a non-Abelian gauge field for the Lorentz group $SO(3,1)$, which is non-compact. The action for General Relativity is linear in the field strength associated to the spin connection, and its equation of motion corresponds to the standard metricity constraint. Consequently, the zero-torsion spin connection is never realized as an independent degree of freedom and is determined by the vierbein field. In this work, we take a different perspective and consider a pure Yang-Mills theory for the spin connection coupled to Dirac fermions, resulting in the former being a dynamical field. After discussing various approaches towards managing the pathologies associated with non-compact gauge theories, we compute the tree-level amplitude for fermion scattering via a spin connection exchange. In contrast to integrating out torsion in the presence of fermions, the model induces a chiral four-Fermi like term that involves a right-right current interaction, which is not present in the Standard Model.
