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 — advanced_tools:group_theory:so_2 [2020/12/12 23:51] (current)edi created 2020/12/12 23:51 edi created 2020/12/12 23:51 edi created Line 1: Line 1: + ====== SO(2) ====== + +  ​ + + 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 $U(1)$. + ​ +  ​ + + **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 }}] + +  ​ + + + The motto in this section is: //the higher the level of abstraction,​ the better//. + ​ + +  ​ + + /​*<​tabbox FAQ>​*/ ​ + + /​*<​tabbox History>​*/ ​ + + ​ +