复数域的新推广及其物理意义  

New Extension of Complex Number Field and Their Physical Meaning

作　　者：张一方[1] 

机构地区：[1]云南大学物理系,云南昆明650091

出　　处：《吉首大学学报（自然科学版）》2008年第5期45-48,共4页Journal of Jishou University(Natural Sciences Edition)

基　　金：国家自然科学基金资助项目(K1020195)

摘　　要：在数系发展的基础上,提出了一种新的发展模式:四元数推广为矩阵形式aI+bA+cB+dC,其中单位矩阵I和3个特殊矩阵A,B,C分别相应于数1和虚数单位i,j,k.它们一般组成环,但3种矩阵aI+bA,aI+cB,aI+dC及某些特殊的二阶甚至高阶矩阵可以组成域,这是一类新的超复数系.最后探讨了这种新数系可能具有的物理意义.Based on a brief review on developments of number system,a new developed pattern is proposed. The quaternion is extended to a matrix form aI＋bA ＋cB ＋dC,in which the identity matrix I and three special matrices A,B,C correspond to number 1 and three units of imaginary number i,j ,k, respectively. They form usually a ring,but some fields may be composed of three matrices aI＋bA ,aI＋cB ,aI＋dC,and of some special 2-order,even n-order matrices. It is a new type of hypercomplex number fields. Finally, the possible physical meaning of the new number system is researched.

关 键 词：数系 矩阵 复数 环 域 物理意义 

分 类 号：O41[理学—理论物理]