Lorentz Transformation

${\begin{aligned}&x{{'}^{\alpha }}=\Lambda _{\beta }^{\alpha }{{x}^{\beta }}+{{a}^{\alpha }}\\&\gamma ={{\left(1-{{\beta }^{2}}\right)}^{-{\frac {1}{2}}}},\beta ={\frac {v}{c}}\\\end{aligned}}$

spezielle

$\Lambda _{0}^{0}=\gamma ,\Lambda _{0}^{i}=\Lambda _{i}^{0}=\gamma {\frac {{v}^{i}}{c}},\Lambda _{k}^{i}={{\delta }_{ik}}+\left(\gamma -1\right){\frac {{{v}^{i}}{{v}^{k}}}{{v}^{2}}}$