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--- advanced_tools:group_theory:so3 [2018/04/15 16:33]
aresmarrero [Concrete]
+++ advanced_tools:group_theory:so3 [2020/11/29 17:17]
edi [Intuitive]
@@ Line 2: / Line 2: @@
 <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.)
-<note tip>
+$SO(3)$ is closely related to the groups $SU(2)$ and $Sp(1)$. They are all locally isomorphic, that is, they have the same Lie algebra.
-Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party.
-</note>
 <tabbox Concrete>
@@ Line 13: / Line 12: @@
 [{{ :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 }}]