已經有許多理論預測了超光速粒子以及超光速運動的相對論。我們在這篇文章中提出了複數勞倫茲對稱 (Complexified Lorentz symmetry)，或稱作複數勞倫茲群 (Complex Lorentz group)，我們將勞倫茲群以及它的群表示 (Representation) 複數化 (Complexify) 後，從三加一維的實數時空變成三加一維的複數向量空間，然後證明它是不可約化(irreducible)。然後我們我們使用 SL(4,C) 的餘空間( Coset space)去找到複數的閔可夫斯基時空 (Complex Minkowski space) 以及複數勞倫茲群如何作用在上面。最後我們定義了複數閔可夫斯基時空的均速運動並將之視為一條複數線並且分類。;There are many theory about faster than light particles, and the new transformation that apply for relative velocities greater than the speed of light. We propose here a complexified Lorentz symmetry, or complex Lorentz group, we complexify Lorentz group and representation from real Lorentz group and 3+1 real space time, and find it is irreducible in 3+1 complex vector space. And we use the coset space of SL(4,C) to find complex Minkowski space and how complex Lorentz group acting on it. Finally we define the uniform motion in complex Minkowski space as complex line and classify it.
