四元数、Clifford代数与超复数及其在物理学中的应用

Quaternion,Clifford Algebra,Hypercomplex Number and Their Applications in Physics

本文是一篇介绍Clifford代数基本性质和应用的文章.Clifford代数是实数、复数、四元数和向量代数的统一和推广,它准确、忠实地刻画了时空的内在性质,为众多数学和物理理论提供了统一、标准、优雅和开放的语言和工具.超复数系有望能够完成现代科学的一次新的大综合,值得在本科物理和数学的教学中普及.

This paper presents some basic properties and applications of Clifford algebra,which is a unification and generalization of complex numbers,quaternions and vector algebra,which accurately and completely describes the intrinsic properties of space-time.Clifford algebra provides a unified,standard,elegant language and tool for many mathematical and physical theories.Hypercomplex number systems have the potential to complete a new large synthesis of modern sciences and it is worthy to be popularized in teaching and scientific research.