论文标题
非官能和物理：非技术评论
Noncommutativity and Physics: A non-technical review
论文作者
论文摘要
我们概述了非共同几何形状对物理学的应用。我们的重点完全放在概念上的思想上，而不是基础技术。从历史上开始，我们将从海森堡的关系开始，我们将解释一般的非交易性如何产生典型的时间演变，同时允许离散和连续变量共存。然后解释了几何形状的光谱方法，以包含两种天然成分：线元素和代数。这两者之间的关系取决于所谓的较高的海森伯格关系，旋转几何形状和非亚伯仪理论都出现了。我们的博览会表明了物理学中的某些应用，包括标准模型以外的pati-salam统一，维度4，第二量化和熵的关键性。
We give an overview of the applications of noncommutative geometry to physics. Our focus is entirely on the conceptual ideas, rather than on the underlying technicalities. Starting historically from the Heisenberg relations, we will explain how in general noncommutativity yields a canonical time evolution, while at the same time allowing for the coexistence of discrete and continuous variables. The spectral approach to geometry is then explained to encompass two natural ingredients: the line element and the algebra. The relation between these two is dictated by so-called higher Heisenberg relations, from which both spin geometry and non-abelian gauge theory emerges. Our exposition indicates some of the applications in physics, including Pati--Salam unification beyond the Standard Model, the criticality of dimension 4, second quantization and entropy.
