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advanced_tools:group_theory:su3
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SU(3)
Intuitive
The Lie group $SU(3)$ describes abstract "rotations" in a space with three complex dimensions. Each "rotation" is characterized by eight abstract "angles".
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.
For more groups and their representations see Fun with Symmetry.
Abstract
The motto in this section is: the higher the level of abstraction, the better.
Why is it interesting?
advanced_tools/group_theory/su3.1609020113.txt.gz · Last modified: 2020/12/26 23:01 by edi
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