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--- advanced_tools:group_theory:lorentz_group [2018/04/06 15:56]
jakobadmin [Concrete]
+++ advanced_tools:group_theory:lorentz_group [2018/04/06 16:01]
jakobadmin [Concrete]
@@ Line 51: / Line 51: @@
 \[ \Lambda_{\mathrm{rot }}= \begin{pmatrix} 1 &  \\ & R_{3 \times 3} \end{pmatrix}
 \]
-with the usual rotation matrices  $R_{3 \times 3}$.
+with the usual rotation matrices  $R_{3 \times 3}$:
+\begin{eqnarray}
+& & R_x(\phi) =
+\begin{pmatrix}
+& 0 & 0 \\ 0 & \cos\phi & \sin\phi \\ 0 & -\sin\phi & \cos\phi
+\end{pmatrix} \label{eq:rotx} \\
+& & R_y(\psi) =
+\begin{pmatrix}
+\cos \psi & 0 & -\sin\psi \\ 0 & 1 & 0 \\ \sin\psi & 0 & \cos\psi
+\end{pmatrix} \label{eq:roty} \\
+& & R_z(\theta) =
+\begin{pmatrix}
+\cos \theta & \sin \theta & 0 \\-\sin\theta & \cos\theta & 0 \\ 0 & 0 & 1
+\end{pmatrix} \label{eq:rotz}
+\end{eqnarray}
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