x ′ α = Λ β α x β + a α γ = ( 1 − β 2 ) − 1 2 , β = v c {\displaystyle {\begin{aligned}&x{{'}^{\alpha }}=\Lambda _{\beta }^{\alpha }{{x}^{\beta }}+{{a}^{\alpha }}\\&\gamma ={{\left(1-{{\beta }^{2}}\right)}^{-{\frac {1}{2}}}},\beta ={\frac {v}{c}}\\\end{aligned}}}
Λ 0 0 = γ , Λ 0 i = Λ i 0 = γ v i c , Λ k i = δ i k + ( γ − 1 ) v i v k v 2 {\displaystyle \Lambda _{0}^{0}=\gamma ,\Lambda _{0}^{i}=\Lambda _{i}^{0}=\gamma {\frac {{v}^{i}}{c}},\Lambda _{k}^{i}={{\delta }_{ik}}+\left(\gamma -1\right){\frac {{{v}^{i}}{{v}^{k}}}{{v}^{2}}}}
