advanced_tools:group_theory:u1

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advanced_tools:group_theory:u1 [2018/05/05 12:37] jakobadmin ↷ Links adapted because of a move operation |
advanced_tools:group_theory:u1 [2020/12/12 23:06] (current) edi [Concrete] |
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Take note that the tangent space of a circle is, of course, just a copy of $\mathbb{R}$ but the isomorphic space $Im \mathbb{C}$ is more convenient because its elements can be "exponentiated" to give the elements $e^{i \theta}$ of $U(1)$. | Take note that the tangent space of a circle is, of course, just a copy of $\mathbb{R}$ but the isomorphic space $Im \mathbb{C}$ is more convenient because its elements can be "exponentiated" to give the elements $e^{i \theta}$ of $U(1)$. | ||

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+ | ---- | ||

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+ | **Representations** | ||

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+ | The diagram below shows the defining representation of $U(1)$ in its upper branch and the conjugate representations of the same group in its lower branch. For a more detailed explanation of this diagram and more representations of $U(1)$ see [[https://esackinger.wordpress.com/|Fun with Symmetry]]. | ||

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+ | [{{ :advanced_tools:group_theory:representation_theory:u1_conj_rep.jpg?nolink }}] | ||

<tabbox Abstract> | <tabbox Abstract> | ||

advanced_tools/group_theory/u1.txt · Last modified: 2020/12/12 23:06 by edi

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