====== Trivial Representation ======

<tabbox Intuitive> 

The trivial representation maps all group elements to the identity element. This representation exists for any group.

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 }}]

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]]. 
 
<tabbox Abstract> 

<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

<tabbox Why is it interesting?>   

/*<tabbox FAQ>*/ 

/*<tabbox History>*/ 

</tabbox>