advanced_tools:group_theory:lie_groups

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

advanced_tools:group_theory:lie_groups [2017/12/17 11:23] |
advanced_tools:group_theory:lie_groups [2017/12/17 12:23] (current) jakobadmin created |
||
---|---|---|---|

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> | ||

+ | |||

+ | 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> | ||

+ | |||

Except where otherwise noted, content on this wiki is licensed under the following license: CC Attribution-Share Alike 4.0 International