一类Minkowski复空间的拟距离和奇异性质

A Class of Quasi-Distance and Singularity of Minkowski Complex Space

双曲虚单位对应一类Minkowski复空间并具有方向异性的特点.四维时空中特殊方向上两时空点间的减法对应类时区与类光区的几何关联,在物理中表示粒子和场的相互作用.通过定义拟(虚)距离使Minkowsk空间的时空映射和间隔不变量进行度量公理化.四维时空中不同方向的距离或度量需要用线度因子和角度因子共同刻画,其中角度因子对应模糊集合,决定了Minkowski度量空间的奇异性质.

Hyperbolic imaginary unit is corresponding to the Minkowski complex space, which possesses directional singularity. In four-dimensional space time, the subtraction between two space-time points in special direction corresponds to the geometric cOrrelation between time-like region and light-like region, and itrepresents the interaction between particles and fields in physics. In the article, we make the spatio-temporal mapping and interval invariant axiomatic by defining quasi-distance. In four-dimensional space time, the distance of different directions can be depicted by both dimension factor and angle factor, where angle factor corresponds to fuzzy set, and determines the singularity of Minkowski complex space.