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--- advanced_tools:group_theory:lie_groups [2017/12/17 11:23]
+++ advanced_tools:group_theory:lie_groups [2023/04/17 03:16] (current)
edi [Student]
@@ Line 1: / Line 1: @@
+====== Lie Groups ======
+<tabbox Why is it interesting?>
+Lie groups describe continuous symmetry and lie at the heart of modern physics. For example, the symmetry group of the [[models:standard_model|standard model of particle physics]] and the best spacetime symmetry group that we know (the Poincare group) are Lie groups.
+<tabbox Layman>
+A Lie group is a continuous set of transformations that satisfy the [[advanced_tools:group_theory:|group axioms]]. A good example for a Lie group is the symmetry group of the circle. A rotation by $5^\circ$ is a symmetry of the circle and a rotation by $0.00001^\circ$ is a symmetry, too. In contrast, the symmetry group of a square is not continuous. A rotation by $90^\circ$ is a symmetry, whereas a rotation by $5^\circ$ is not a symmetry.
+<tabbox Student>
+The diagram below shows some low-dimensional, but important, Lie groups and their relationships.
+[{{ :advanced_tools:group_theory:group_relations.jpg?nolink }}]
+For a more detailed explanation of this diagram and much more, see [[https://esackinger.wordpress.com/blog/lie-groups-and-their-representations/#group_relations|Fun with Symmetry]].
+----
+For book recommendations, see [[advanced_tools:group_theory|here]].
+<tabbox Researcher>
+<note tip>
+The motto in this section is: //the higher the level of abstraction, the better//.
+</note>
+<tabbox Examples>
+--> Example1#
+<--
+--> Example2:#
+<--
+<tabbox FAQ>
+<tabbox History>
+</tabbox>

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