✎ Trivial Representation [The Physics Travel Guide]

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

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

Spin-$0$ particles/fields transform under the trivial representation of SU(2). That is, their spin value does no depend on orientation in space.

The action transforms under the trivial representation of space-time and gauge symmetry groups. That is, the action does not depend on these symmetry transformations.

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**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/|Fun with Symmetry]]. 
 
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<note tip>
The motto in this section is: //the higher the level of abstraction, the better//.
</note>

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