advanced_tools:group_theory:representation_theory:dual_representation
| Both sides previous revision Previous revision | Next revision Both sides next revision | ||
|
advanced_tools:group_theory:representation_theory:dual_representation [2022/07/03 20:36] edi [Concrete] |
advanced_tools:group_theory:representation_theory:dual_representation [2022/07/03 20:38] edi [Concrete] |
||
|---|---|---|---|
| Line 11: | Line 11: | ||
| **Example** | **Example** | ||
| - | The diagram below shows the defining representation of $SU(2)$ in its upper branch. To construct the dual representation, we let it act on the dual vector space, that is, the space of covectors. In this example, the dual representation is the same as the complex-conjugate representation. Moreover, the defining and complex-conjugate representations of $SU(2)$ are equivalent, that is, there is a similarity transformation that takes one to the other. | + | The diagram below shows the defining representation of $SU(2)$ in its upper branch. To construct the dual representation, we let it act on the dual vector space, that is, the space of covectors. In this example, the dual representation is the same as the complex-conjugate representation ($\tilde{U}=U^*$). Moreover, the defining and complex-conjugate representations of $SU(2)$ are equivalent, that is, there is a similarity transformation that takes one to the other. |
| [{{ :advanced_tools:group_theory:representation_theory:su2_dual.jpg?nolink }}] | [{{ :advanced_tools:group_theory:representation_theory:su2_dual.jpg?nolink }}] | ||
advanced_tools/group_theory/representation_theory/dual_representation.txt ยท Last modified: 2023/03/19 21:42 by edi
Page Tools
Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International
