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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] Both sides previous revision Previous revision 2020/12/05 18:39 edi [Intuitive] 2020/11/29 17:59 edi [Concrete] 2020/11/29 17:17 edi [Intuitive] 2020/11/28 18:16 edi [Concrete] 2018/04/15 16:33 aresmarrero [Concrete] 2018/04/15 16:33 aresmarrero [Concrete] 2018/04/15 16:32 aresmarrero created 2020/12/05 18:39 edi [Intuitive] 2020/11/29 17:59 edi [Concrete] 2020/11/29 17:17 edi [Intuitive] 2020/11/28 18:16 edi [Concrete] 2018/04/15 16:33 aresmarrero [Concrete] 2018/04/15 16:33 aresmarrero [Concrete] 2018/04/15 16:32 aresmarrero created Line 2: Line 2:  ​  ​ - 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.