Timeline for What is the importance of $SU(2)$ being the double cover of $SO(3)$?
Current License: CC BY-SA 4.0
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| Dec 3 at 0:00 | history | bumped | CommunityBot | This question has answers that may be good or bad; the system has marked it active so that they can be reviewed. | |
| Jun 30 at 7:30 | comment | added | Valter Moretti | This could be of interest, especially my answer physics.stackexchange.com/q/808910 | |
| Jun 30 at 6:57 | answer | added | Mozibur Ullah | timeline score: 0 | |
| Jun 30 at 6:33 | comment | added | Qmechanic♦ | More on $SO(3)$ & $SU(2)$. | |
| Jun 30 at 5:47 | comment | added | Plop | Do you expect an answer to contain much more than « double covers are the easiest connected ones (because they minimize the cardinal of fibers) so we are lucky that some groups we study are as close as possible to be simply-connected »? | |
| Jun 30 at 5:43 | comment | added | Marius Ladegård Meyer | Agreed! I don't doubt a good answer will be mostly mathematical ;) | |
| Jun 30 at 5:43 | history | edited | Silly Goose | CC BY-SA 4.0 |
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| Jun 30 at 5:41 | comment | added | Silly Goose | I see what you mean. I am interested in the physical importance, so I will clarify that in the post. But to also clarify, I would like an answer in terms of the relevant mathematics. I think to me the two are quite intertwined. For instance, a satisfactory answer to the question of "what are spin-$j$ systems" would involve talking about how to classify irreducible projective representations of $SO(3)$. Assuming one knows introductory quantum mechanics, the only physics there is defining the correspondence between physical and mathematical objects. @MariusLadegårdMeyer | |
| Jun 30 at 5:37 | comment | added | Marius Ladegård Meyer | Sure, but it's still a maths question :) As an analogy, if people on this site discuss chemical bonds in relation to the physics of phases of matter, I might wonder about something since I have never studied chemistry. But posting a question purely about chemistry here would still be off-topic imho. Again, just want to clarify if you are interested in the physical or mathematical importance of the things you are asking about. | |
| Jun 30 at 5:34 | comment | added | Silly Goose | To add to my comment above, it seems like people often (perhaps wrongly) cite $SU(2)$ being the double cover of $SO(3)$ as being responsible for consequences that are really consequences of $SU(2)$ being the (isomorphic to) universal cover of $SO(3)$. | |
| Jun 30 at 5:29 | comment | added | Silly Goose | People on this site commonly cite $SU(2)$ being the double cover of $SO(3)$ as a primary point of importance, especially in the context of talking about irreducible projective representations of $SO(3)$. I would like to understand what they mean. So, I think the answer is "yes" to your comment. @MariusLadegårdMeyer. | |
| Jun 30 at 5:22 | history | edited | Qmechanic♦ |
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| Jun 30 at 5:21 | comment | added | Marius Ladegård Meyer | As stated this is a question exclusively about math, so should be asked on that SE. Are you wondering about physical importance of the double cover? | |
| Jun 30 at 5:11 | history | edited | Silly Goose | CC BY-SA 4.0 |
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| Jun 30 at 5:00 | history | asked | Silly Goose | CC BY-SA 4.0 |