advanced_tools:group_theory:so_2

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+ | ====== SO(2) ====== | ||

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+ | <tabbox Intuitive> | ||

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+ | 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. | ||

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+ | The group $SO(2)$ is isomorphic to $U(1)$. | ||

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+ | <tabbox Concrete> | ||

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+ | **Representations** | ||

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+ | 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]]. | ||

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+ | [{{ :advanced_tools:group_theory:representation_theory:so2_2d_4d_reps.jpg?nolink }}] | ||

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+ | <tabbox Abstract> | ||

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+ | <note tip> | ||

+ | The motto in this section is: //the higher the level of abstraction, the better//. | ||

+ | </note> | ||

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+ | <tabbox Why is it interesting?> | ||

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+ | /*<tabbox FAQ>*/ | ||

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+ | /*<tabbox History>*/ | ||

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+ | </tabbox> | ||

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advanced_tools/group_theory/so_2.txt ยท Last modified: 2020/12/12 23:51 by edi

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