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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** 
 + 
 +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]]. 
 + 
 +[{{ :​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