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advanced_tools:group_theory:lie_groups [2017/12/17 10:23] (current)
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 +====== 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> ​
 +
 +See the recommendations [[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>​
 +
  
advanced_tools/group_theory/lie_groups.txt ยท Last modified: 2017/12/17 10:23 (external edit)