Differences

This shows you the differences between two versions of the page.

--- advanced_tools:group_theory:representation_theory:adjoint_representation [2018/04/15 16:38]
aresmarrero [Concrete]
+++ advanced_tools:group_theory:representation_theory:adjoint_representation [2020/11/29 16:24]
edi [Intuitive]
@@ Line 2: / Line 2: @@
 <tabbox Intuitive>
+The adjoint representation describes how the generators of the group, which live in the Lie algebra, transform. In other words, the adjoint representation acts on the Lie algebra. Note that the Lie algebra is a regular vector space and thus can serve as a representation space.
-<note tip>
+The dimensionality of the adjoint representation is equal to that of the Lie algebra. For example, the adjoint representation of $SU(2)$ is 3 dimensional and the adjoint representation of $SU(3)$ is 8 dimensional.
-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>
+An important application of the adjoint representation is the transformation of gauge fields.
 <tabbox Concrete>
   * For a detailed discussion, see [[http://jakobschwichtenberg.com/adjoint-representation/|What’s so special about the adjoint representation of a Lie group?]] by J. Schwichtenberg