advanced_tools:group_theory:su3
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advanced_tools:group_theory:su3 [2018/04/15 16:32] aresmarrero created |
advanced_tools:group_theory:su3 [2023/04/17 03:20] (current) edi [Intuitive] |
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| <tabbox Intuitive> | <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. | |
| - | <note tip> | + | |
| - | 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> | + | |
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| <tabbox Concrete> | <tabbox Concrete> | ||
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| **Representations** | **Representations** | ||
| - | [{{ :advanced_tools:group_theory:su3reps.png?nolink |Diagram by Eduard Sackinger}}] | + | 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. |
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| + | [{{ :advanced_tools:group_theory:representation_theory:su3_adjoint.jpg?nolink }}] | ||
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| + | For more groups and their representations see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/|Fun with Symmetry]]. | ||
| <tabbox Abstract> | <tabbox Abstract> | ||
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| </note> | </note> | ||
| - | <tabbox Why is it interesting?> | + | <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). | ||
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| + | $SU(3)$ is also the gauge group of the strong nuclear interaction. It describes how particles with "color charge" (quarks and gluons) interact. | ||
advanced_tools/group_theory/su3.1523802741.txt.gz · Last modified: 2018/04/15 14:32 (external edit)
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