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advanced_tools:group_theory:lorentz_group [2018/04/06 15:56] jakobadmin [Concrete] |
advanced_tools:group_theory:lorentz_group [2018/05/04 09:53] jakobadmin ↷ Links adapted because of a move operation |
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\[ \Lambda_{\mathrm{rot }}= \begin{pmatrix} 1 & \\ & R_{3 \times 3} \end{pmatrix} | \[ \Lambda_{\mathrm{rot }}= \begin{pmatrix} 1 & \\ & R_{3 \times 3} \end{pmatrix} | ||
\] | \] | ||
- | 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} | ||
+ | 1 & 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} | ||
__Boosts__ | __Boosts__ |