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![[parent]](https://images.physicslibrary.org/images/uparrow.png) Viewing Message
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| ``Re: Why we can say a spinor be a representation of SU(2)?''
by Tyger on 2007-03-01 23:39:51 |
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| > ... It's due to
> bad agreed terminology amongst physicists and
> mathematicians.
Fine, this sounds reasonable.
>I think it's because that once you've
> figured out the eigenstates or eigenvectors which are
> spinors, then you can work out the whole representation.
>
> Read pg. 23 for more details
>
> http://paul.metcalfe.googlepages.com/fqm.pdf
This book explains somewhat "on what space of states can this algebra of operators be realized, or alternatively, what are the representations", that's nice. However, I'm afraid I found some mistakes in it, only after a simple skim. For example, in page 23, it read: $[J_\pm,J_3]=\pm J_\pm$, however the correct equation should be
$[J_3,J_\pm]=\pm J_\pm$. And about the first line of page 24, it read: Using the $[J_\pm,J_3]$ relation we have $J_3 J_\pm = J_\pm J_3 \pm J_3$, that's incorrect too, it should be $J_3 J_\pm = J_\pm J_3 \pm J_\pm$.
> Hope it helps.
Yes, your answer is really helpful. It helps me to understand more deeply why some representations be constructed like what we see today, and why some terminologies be selected. Thanks.
Tyger
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