LIE-GROUPS AS SPIN GROUPS

被引：82

作者：

DORAN, C

HESTENES, D

SOMMEN, F

VANACKER, N

机构：

[1] ARIZONA STATE UNIV,DEPT PHYS & ASTRON,TEMPE,AZ 85287

[2] STATE UNIV GHENT,DEPT MATH ANALYSIS,B-9000 GHENT,BELGIUM

来源：

JOURNAL OF MATHEMATICAL PHYSICS | 1993年 / 34卷 / 08期

关键词：

D O I：

10.1063/1.530050

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

It is shown that every Lie algebra can be represented as a bivector algebra; hence every Lie group can be represented as a spin group. Thus, the computational power of geometric algebra is available to simplify the analysis and applications of Lie groups and Lie algebras. The spin version of the general linear group is thoroughly analyzed, and an invariant method for constructing real spin representations of other classical groups is developed. Moreover, it is demonstrated that every linear transformation can be represented as a monomial of vectors in geometric algebra.

引用

页码：3642 / 3669

页数：28