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advanced_tools:group_theory:so_2 [2020/12/12 23:51] (current)
edi created
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 +====== SO(2) ======
 +
 +<tabbox Intuitive> ​
 +
 +The Lie group $SO(2)$ describes all possible 2D rotations. The group is one dimensional,​ that is, it has only one parameter: the rotation angle.
 +
 +The group $SO(2)$ is isomorphic to $U(1)$.
 +  ​
 +<tabbox Concrete> ​
 +
 +**Representations**
 +
 +The diagram below shows the (2-dimensional) defining representation of $SO(2)$ in its upper branch and a 4-dimensional,​ reducible representation of the same group in the lower branch. For a more detailed explanation of this diagram and representations of other Lie groups see [[https://​esackinger.wordpress.com/​|Fun with Symmetry]].
 +
 +[{{ :​advanced_tools:​group_theory:​representation_theory:​so2_2d_4d_reps.jpg?​nolink }}]
 + 
 +<tabbox Abstract> ​
 +
 +<note tip>
 +The motto in this section is: //the higher the level of abstraction,​ the better//.
 +</​note>​
 +
 +<tabbox Why is it interesting?> ​  
 +
 +/​*<​tabbox FAQ>​*/ ​
 +
 +/​*<​tabbox History>​*/ ​
 +
 +</​tabbox>​
 +
  
advanced_tools/group_theory/so_2.txt ยท Last modified: 2020/12/12 23:51 by edi