标题： 从蒙日到希格斯：非交换几何中距离计算的调查 显示英文标题

标题： From Monge to Higgs: a survey of distance computations in noncommutative geometry

摘要： 这是一篇关于非交换几何中Connes距离显式计算的综述，涵盖了有限维谱三元组、准交换几何以及紧算子代数上的谱三元组等内容。 文中还涉及了多个物理应用，例如Higgs场的度量解释，以及与量子时空各种模型中出现的最小长度的比较。 此外，文章研究了与其他数学领域的联系，特别是次黎曼几何中的水平距离。 同时，文章还讨论了将Connes距离解释为最优传输中Monge-Kantorovich度量的非交换版本。 显示英文摘要

摘要： This is a review of explicit computations of Connes distance in noncommutative geometry, covering finite dimensional spectral triples, almost-commutative geometries, and spectral triples on the algebra of compact operators. Several applications to physics are covered, like the metric interpretation of the Higgs field, and the comparison of Connes distance with the minimal length that emerges in various models of quantum spacetime. Links with other areas of mathematics are studied, in particular the horizontal distance in sub-Riemannian geometry. The interpretation of Connes distance as a noncommutative version of the Monge-Kantorovich metric in optimal transport is also discussed.