Timeline for Why the Gell-Mann matrices in the SU(3)-model need to be trace orthogonal?
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
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| Mar 13, 2012 at 21:43 | vote | accept | HAJV | ||
| Mar 13, 2012 at 21:43 | vote | accept | HAJV | ||
| Mar 13, 2012 at 21:43 | |||||
| Mar 11, 2012 at 22:05 | answer | added | user26872 | timeline score: 1 | |
| Feb 24, 2012 at 5:32 | comment | added | Theo Johnson-Freyd | @HAJV: Yemon and Will have already alluded to this, but this question is not acceptable as written. More than anything, it's extremely good practice for you to write details in your question. I vaguely remember the Gell-Mann matrices, and can easily google for them, but that's not the point. You could learn a lot about them just by taking the time to write down everything you know — or, rather, not everything, but one or two well-written paragraphs explaining your question. Once you have put this effort in, please flag for moderator attention and ask your question be reopened. I vote to close. | |
| Feb 23, 2012 at 23:35 | comment | added | Will Jagy | @Cristi, you might as well put your comments together as an answer, comments after the first five get hidden and may never be noticed. The exception is when comments are upvoted, then the top five voted comments appear in chronological order. Of course, anyone can click on "show me more comments" if they have the energy. | |
| Feb 23, 2012 at 23:22 | comment | added | Cristi Stoica | My first guess is that the trace orthogonality property for rep 3 is related to the Killing form (which is defined by the adjoint rep 8). Maybe this makes them ideal for making the root diagrams represent particles with their properties. Gell-Mann started with diagrams representing hadrons, and he choose his matrices so that their action transforms one hadron in another, by increasing or decreasing certain numbers associated to the particles. So, in fact, the representation was provided by nature. | |
| Feb 23, 2012 at 23:14 | comment | added | Cristi Stoica | I think this question is interesting. If the question is simple, then it is easy to provide a link or a reference containing the explanation, but most sources just mention that Gell-Mann wanted his matrices to have similar properties to those of Pauli. I think the question is as clear as possible, especially after the Lie Algebras tag was added. | |
| Feb 23, 2012 at 23:05 | comment | added | Cristi Stoica | It's not about having the trace 0, it is why these matrices were chosen so that $tr(\lambda_i\lambda_j)=2\delta_{ij}$. | |
| Feb 23, 2012 at 23:05 | history | edited | Yemon Choi |
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| Feb 23, 2012 at 23:04 | comment | added | Yemon Choi | mathoverflow.net/howtoask Since not everyone has the same background as you, or uses the same terminology, it is good manners to explain such things. For instance, now that you have provided a link, it seems that the key words are "Lie algebra". | |
| Feb 23, 2012 at 22:42 | comment | added | Will Jagy | We do answer questions at grad student level, even some at undergraduate level. However, we do not really do tutorials. Also, it is desirable that you put in more effort than us. This is a site for professional researchers. The additional reasons for you to put in more background are to show that you have done more work than absolutely nothing, and that you already know more than absolutely nothing. So far you are batting zero. | |
| Feb 23, 2012 at 21:48 | comment | added | HAJV | Those are a representation of the generators of the special unitary group SU(3). I could explain, but not better than you can find at en.wikipedia.org/wiki/Gell-Mann_matrices | |
| Feb 23, 2012 at 21:27 | comment | added | Yemon Choi | Could you please flesh out your question? What are the Gell-Mann matrices? are they uniquely defined objects, or merely a collection that satisfies certain conditions? | |
| Feb 23, 2012 at 21:10 | history | asked | HAJV | CC BY-SA 3.0 |