从张量概念到张量分析

On Tensor:from Concept to Analysis

张量分析是现代数学物理学的基础工具。从广义相对论开始,到规范场论,以至后来的弦理论的建立都得力于张量分析。张量分析所提供的对曲线坐标系的微分方法,真正实现了非欧几何从概念到演算的革命,而所有这一切都是以张量概念的产生为基础的,黎曼的新几何学观念是张量概念产生的原动力之一。另一方面,黎曼几何学与张量分析的交织发展体现在许多方面,文章描绘这两者从起源到成熟的过程中互相促进的历史。

Tensor analysis is a basic method for modern mathematic physics.The general theory of relativity,the gauge theory and the superstring theory are all founded on tensor analysis.On the basis of the concept of tensor,tensor analysis offers differential coefficient method for curvilinear system of coordinates,which has actually realized a revolution for Non-Euclidean geometry from concept to figure.Herein,this paper puts emphasis on the forming and development of tensor analysis.Search for its historical clues in original literatures and textual research.