✎ SO(3) [The Physics Travel Guide]

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====== SO(3) ======

<tabbox Intuitive> 
The Lie group $SO(3)$ describes all possible rotations in 3-dimensional Euclidean space. It thus describes an important symmetry of the physical space we live in. (Other symmetries of our space are translations and boosts.)

$SO(3)$ is closely related to the groups $SU(2)$ and $Sp(1)$. They are all locally isomorphic, that is, they have the same Lie algebra.
  
<tabbox Concrete> 
**Representations**

[{{ :advanced_tools:group_theory:so3reps.png?nolink |Diagram by Eduard Sackinger}}]

----

The diagram below shows the defining 3-dimensional representation of $SO(3)$ in its upper branch. A 5-dimensional representations of the same group is shown in the lower branch. For an explanation of this diagram and more representations of $SO(3)$ see [[https://esackinger.wordpress.com/|Fun with Symmetry]].

[{{ :so3_3d_5d_reps.jpg?nolink }}]

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

</tabbox>

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