====== SU(3) ======

<tabbox Intuitive> 
The Lie group $SU(3)$ describes abstract "rotations" in a space with three complex dimensions. A "rotation" is characterized by eight abstract "angles" or parameters.
 
<tabbox Concrete> 
**Representations**

The diagram below shows the defining (3-dimensional) representation of $SU(3)$ in its upper branch and the 8-dimensional adjoint representations of the same group in its lower branch. The adjoint representation can be rewritten such that it acts on 8-dimensional vectors (as opposed to 3x3 matrices) by regular matrix-vector multiplication.

[{{ :advanced_tools:group_theory:representation_theory:su3_adjoint.jpg?nolink }}]

For more groups and their representations see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/|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?> 
$SU(3)$ is at the heart of the so-called "eightfold way", a scheme that organizes the large "zoo" of hadron particles into neat geometrical patterns (octets and decuplets).

$SU(3)$ is also the gauge group of the strong nuclear interaction. It describes how particles with "color charge" (quarks and gluons) interact. 



</tabbox>