Lorentz Transformation

$\begin{array}{rl}& x{\text{'}}^{\alpha }={\mathrm{\Lambda }}_{\beta }^{\alpha }{x}^{\beta }+a^{\alpha }\\ & \gamma ={(1-{\beta }^2)}^{-\frac{1}{2}},\beta =\frac{v}{c}\\ \end{array}$

spezielle

${\mathrm{\Lambda }}_0^0=\gamma ,{\mathrm{\Lambda }}_0^i={\mathrm{\Lambda }}_i^0=\gamma \frac{v^i}{c},{\mathrm{\Lambda }}_k^i={\delta }_{ik}+(\gamma -1)\frac{v^i{v}^k}{v^2}$