Clifford代数中的双曲相位变换群及其在四维相对论时空中的应用

将Clifford代数所定义的双曲复空间R_H和作用在双曲复空间R_H上的双曲相位变换群U₄(H)赋予了明确的物理意义. 双曲复空间R_H同构于四维Minkowski时空，而其上的双曲相位变换群U₄(H)就是四维相对论时空中的洛仑兹(Lorentz)变换群. 进一步，利用U₄(H)群的复合变换性质，自然导出了四维Minkowski时空中Lorentz变换和速度变换的一般表达式. 由此，将狭义相对论中的特殊Lorentz变换作为特例包含其中. 关键词： 双曲复数 双曲相位变换 Minkowski时空 Clifford代数

Hyperbolic phase transformation group and its applicaton to four-dimensional relativistic spacetime

The hyperbolic complex space R_H defined by the Clifford algebra and the hyperbolic phase transformation group U₄(H) acting on R_H are endowed with definite physical meaning in this paper. The hyperbolic complex space R_H is isomorphic to the 4-dimensional(4D) Minkowski spacetime, and the hyperbolic phase transformation group U₄(H) in R_H is just Lorentz transformation group on 4D relativistic spacetime. Furthermore, the general expressions of Lorentz transformation and the velocity transformation on 4D Minkowski spacetime are naturally derived using the composite transformations of the group U₄(H). Hence, the well-known special Lorentz transformation in the special relativity(SR) is contained as a special case in our discussions.