标题： 洛伦兹非交换几何方法 显示英文标题

标题： Lorentzian approach to noncommutative geometry

摘要： 本论文研究了 Alain Connes 的非交换几何学的洛伦兹广义化。 第一章中，我们在统一理论的背景下介绍了非交换几何学的概念。 第二章专门介绍非交换几何学的基本要素，包括非交换积分、黎曼距离函数和谱三元组。 最后一章探讨了向洛伦兹流形推广的问题。我们通过全局时空中类光欧几里得条件的第一步推广了距离函数。然后，我们提出了时间洛伦兹谱三元组的第一个公理，作为伪黎曼谱三元组的推广，并结合了非交换几何中的全局时间概念。 显示英文摘要

摘要： This thesis concerns the research on a Lorentzian generalization of Alain Connes' noncommutative geometry. In the first chapter, we present an introduction to noncommutative geometry within the context of unification theories. The second chapter is dedicated to the basic elements of noncommutative geometry as the noncommutative integral, the Riemannian distance function and spectral triples. In the last chapter, we investigate the problem of the generalization to Lorentzian manifolds. We present a first step of generalization of the distance function with the use of a global timelike eikonal condition. Then we set the first axioms of a temporal Lorentzian spectral triple as a generalization of a pseudo-Riemannian spectral triple together with a notion of global time in noncommutative geometry.