This shows you the differences between two versions of the page.
Both sides previous revision Previous revision Next revision | Previous revision Next revision Both sides next revision | ||
advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2022/07/03 19:46] edi |
advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2023/02/20 18:48] edi [Intuitive] |
||
---|---|---|---|
Line 3: | Line 3: | ||
<tabbox Intuitive> | <tabbox Intuitive> | ||
- | <note tip> | + | The trivial representation maps all group elements to the identity matrix. This representation exists for any group. |
- | Explanations in this section should contain no formulas, but instead colloquial things like you would hear them during a coffee break or at a cocktail party. | + | |
- | </note> | + | Spin-$0$ particles and fields transform under the trivial representation of $SU(2)$. That is, their spin value does not change under rotation. |
+ | |||
+ | The action (and often the Lagrangian) transforms under the trivial representation of the Lorentz group and the relevant gauge groups. That is, the action is not affected by these symmetry transformations. | ||
| | ||
<tabbox Concrete> | <tabbox Concrete> | ||
+ | **Example** | ||
+ | |||
+ | The diagram below shows the defining representation of $SU(2)$ in its upper branch and the trivial (1-dimensional) representation in its lower branch. | ||
+ | |||
+ | [{{ :advanced_tools:group_theory:representation_theory:su2_1d_rep.jpg?nolink }}] | ||
- | <note tip> | + | For a more detailed explanation of this diagram see [[https://esackinger.wordpress.com/|Fun with Symmetry]]. |
- | In this section things should be explained by analogy and with pictures and, if necessary, some formulas. | + | |
- | </note> | + | |
<tabbox Abstract> | <tabbox Abstract> |