论文标题
将非交通性几何形状与高能量物理的应用
Twisting Noncommutative Geometries with Applications to High Energy Physics
论文作者
论文摘要
凭借非交通性几何形状的裸露必需品（由光谱三重），我们首先描述了它如何自然产生衡量理论。然后，我们迅速回顾了扭曲的概念（尤其是最小）非交通性几何形状以及它如何诱导灯芯旋转，即从欧几里得人向洛伦兹的度量标志的过渡。我们专注于相对较大的光谱三元示例。例如对应于封闭的Riemannian自旋歧管，$ u（1）$量表理论和电动力学的。通过最小化这些示例并计算其相关的费米子动作，我们演示了如何在Lorentz签名中达到与物理相关的动作（例如Weyl和Dirac动作），即使从欧几里得光谱三元组开始。在此过程中，我们不仅提取了对扭曲的物理解释，而且还准确地捕获了灯芯旋转在费米金动作水平上的发生。
With the bare essentials of noncommutative geometry (defined by a spectral triple), we first describe how it naturally gives rise to gauge theories. Then, we quickly review the notion of twisting (in particular, minimally) noncommutative geometries and how it induces a Wick rotation, that is, a transition of the metric signature from euclidean to Lorentzian. We focus on comparatively more tractable examples of spectral triples; such as the ones corresponding to a closed Riemannian spin manifold, $U(1)$ gauge theory, and electrodynamics. By minimally twisting these examples and computing their associated fermionic actions, we demonstrate how to arrive at physically relevant actions (such as the Weyl and Dirac actions) in Lorentz signature, even though starting from euclidean spectral triples. In the process, not only do we extract a physical interpretation of the twist, but we also capture exactly how the Wick rotation takes place at the level of the fermionic action.
