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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] Both sides previous revision Previous revision 2020/09/07 04:19 [Concrete] 2018/04/15 16:31 aresmarrero 2018/04/15 16:30 aresmarrero [Student] 2018/03/17 16:03 jakobadmin [Student] 2018/03/17 16:02 jakobadmin [Student] 2018/03/17 16:01 jakobadmin [Student] 2017/12/17 12:02 jakobadmin [Why is it interesting?] 2017/12/17 11:59 jakobadmin [Student] 2017/12/04 09:01 external edit2017/11/03 14:10 jakobadmin created 2020/09/07 04:19 [Concrete] 2018/04/15 16:31 aresmarrero 2018/04/15 16:30 aresmarrero [Student] 2018/03/17 16:03 jakobadmin [Student] 2018/03/17 16:02 jakobadmin [Student] 2018/03/17 16:01 jakobadmin [Student] 2017/12/17 12:02 jakobadmin [Why is it interesting?] 2017/12/17 11:59 jakobadmin [Student] 2017/12/04 09:01 external edit2017/11/03 14:10 jakobadmin created Line 20: Line 20: 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. 