Why $SU(2)$ and $SO(3)$ share the same Lie algebra?
2020年5月13日 · Thus, it's true that the basis elements are the same (so of course they follow the same commutation relations) but it's also true that the vector space of the SU(2) Lie algebra is …
group theory - how to show $SU(2)/\mathbb{Z}_2\cong SO(3 ...
To prove surjectivity, you can use that SO(3) is connected and that the quotient map sends a small neighborhood of the identity in SU(2) to a small neighborhood of the identity of SO(3), so …
Map between $SU(2)$ and $SO(3)$ - Mathematics Stack Exchange
2023年12月29日 · With all due respect to Manton, if that is indeed what he does, defining the map from $\mathrm{SU}_2$ to $\mathrm{SO}_3$ by this formula is a god-awful way to describe the …
How to construct the Lie group homomorphism $SU(2) \to SO(3)
In principle it is enough to take the exponential of the Lie algebra isomorphism and a surjective Lie group homomorphism arises this way $\phi : SU(2)\to SO(3)$: $$\phi\left(\exp\left\{-\sum_k t^k …
lie groups - Proof help: $SU(2)$ is a double cover of $SO(3 ...
2014年12月6日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
The role of SO (3) and SU (2) in quantum mechanics [duplicate]
In fact $\mathrm{SU}(2)$ is the double cover of $\mathrm{SO}(3)$; there is a 2-1 homomorphism from the former to the latter. How is this possible when every so(3) irrep can get raised to one …
differential geometry - Why is $SU(2)$ diffeomorphic to $S^3 ...
$\begingroup$ You seem to be confusing $\operatorname{SU}(2)$ with its algebra $\mathfrak{su}(2)$; besides, you can very easily check that any Pauli matrix $\sigma_j$ has a …
Understanding SU(2) and SO(3) Representations - Physics Forums
2018年3月31日 · I read that SU(2) is the double covering of SO(3), so to each matrix in SO(3) corresponds one in SU(2). I am not sure I understand this. So if we have a 3D representation …
rotations - On the relation between SO(3) and SU(2) groups ...
2020年4月8日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
$S^2=SO(3)/SO(2)$. Does this mean that $S^2 = SU(2)/U(1)
2015年3月26日 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …