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advanced_tools:group_theory:su2

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advanced_tools:group_theory:su2 [2018/04/15 16:31]
aresmarrero
advanced_tools:group_theory:su2 [2020/09/07 04:19] (current)
14.161.7.200 [Concrete]
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 Elements of $SU(2)$ can be written as Elements of $SU(2)$ can be written as
  
-$$ U(x) = e^{i a \vec{r} \vec{\sigma} }= e^{i a \vec{r} \vec{\sigma}} = \cos(a) + i \vec{r} \vec{\sigma} \sin( a )$$+$$ U(x) = e^{i a \vec{r} \vec{\sigma} } = \cos(a) + i \vec{r} \vec{\sigma} \sin( a )$$
  
-where $\vec{\sigma}=(\sigma_1,​\sigma_2,​\sigma_3)$ are the usual Pauli matrices and $ \vec{r} $ is a unit vector.+where $\vec{\sigma}=(\sigma_1,​\sigma_2,​\sigma_3)$ are the usual Pauli matrices and $ \vec{r} $ is a unit vector. This is also known as the version of the the well-known Euler'​s identity for $2\times2$ matrices.
  
  
advanced_tools/group_theory/su2.txt ยท Last modified: 2020/09/07 04:19 by 14.161.7.200