Exotic smoothness and physics
Exotic smoothness and physics
复制标题
奇异的平滑度和物理特性
DOI：
10.1063/1.530761
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发表时间：
1994
影响因子：
1.3
通讯作者：
C. Brans
中科院分区：
文献类型：
--
作者：
C. Brans
最近的数学发现，拓扑平凡的时空模型，特别是最简单的一个，R4，具有丰富的多样性，其中没有两个是同构的，从而标准的，这样的结构在物理学中所发挥的重要作用进行了审查。这意味着物理学可以为时空模型提供一整套新的结构。这些可以被认为是新的全局特征的来源，但不是正确的拓扑特征。本文回顾了一些背景微分拓扑学的讨论的作用，其中一个微分结构必须发挥在任何物理理论的声明，回顾说，同构的核心是广义相对论的原则。一些关于发现外来物种的历史，非标准的，可微的结构进行审查。文中还描述了一些新的结果，并对这些奇异结构的空间局域化进行了推测。
The essential role played by differentiable structures in physics is reviewed in light of recent mathematical discoveries that topologically trivial space–time models, especially the simplest one, R4, possess a rich multiplicity of such structures, no two of which are diffeomorphic to each other and thus to the standard one. This means that physics has available to it a new panoply of structures for space–time models. These can be thought of as a source of new global, but not properly topological, features. This article reviews some background differential topology together with a discussion of the role which a differentiable structure necessarily plays in the statement of any physical theory, recalling that diffeomorphisms are at the heart of the principle of general relativity. Some of the history of the discovery of exotic, i.e., nonstandard, differentiable structures is reviewed. Some new results suggesting the spatial localization of such exotic structures are described and speculations are made on t...