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] edi [Intuitive] |
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| - | 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: 2023/04/17 03:28 by edi
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