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advanced_tools:group_theory:so3

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advanced_tools:group_theory:so3 [2020/11/29 17:59]
edi [Concrete]
advanced_tools:group_theory:so3 [2020/12/05 18:39] (current)
edi [Intuitive]
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 <tabbox Intuitive> ​ <tabbox Intuitive> ​
-The Lie group $SO(3)$ describes all possible rotations in 3-dimensional Euclidean space. It thus describes an important symmetry of the physical space we live in. (Other symmetries ​of our space are translations and boosts.)+The Lie group $SO(3)$ describes all possible rotations ​of an object ​in 3-dimensional Euclidean space. It thus describes an important symmetry of the physical space we live in. (Other ​important spacetime ​symmetries are translations and boosts.)
  
 $SO(3)$ is closely related to the groups $SU(2)$ and $Sp(1)$. They are all locally isomorphic, that is, they have the same Lie algebra. $SO(3)$ is closely related to the groups $SU(2)$ and $Sp(1)$. They are all locally isomorphic, that is, they have the same Lie algebra.
advanced_tools/group_theory/so3.txt ยท Last modified: 2020/12/05 18:39 by edi