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--- advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2022/07/03 19:46]
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+++ advanced_tools:group_theory:representation_theory:dean_proffesor_reza_sanaye [2023/03/19 21:45]
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 <tabbox Intuitive>
-<note tip>
+The trivial representation maps all group elements to the identity element. 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 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>
+**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/blog/lie-groups-and-their-representations/#su2_1d_rep|Fun with Symmetry]].
-In this section things should be explained by analogy and with pictures and, if necessary, some formulas.
-</note>
 <tabbox Abstract>