Take the 2-minute tour ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.

Can somebody explain in a simple way why, talking about representations $$3\otimes3\otimes3=1\oplus8\oplus8\oplus10~?$$

Here $3$ and $\bar{3}$ are the fundamental and anti-fundamental of $SU(3)$, in this case.

share|improve this question
3  
Related $SU(3)$ post: physics.stackexchange.com/q/10403/2451 especially the answer physics.stackexchange.com/a/14586/2451 . Do you know Clebsch-Gordan decomposition of $SU(2)$ irreps? See e.g. physics.stackexchange.com/q/16098/2451 . –  Qmechanic Mar 21 '13 at 17:29
4  
I found the group theory appendix (B) in Zee, Quantum Field Theory in a Nutshell, to be helpful for this stuff. –  Michael Brown Mar 22 '13 at 0:19
    
Removed subquestions that are duplicates in v3: physics.stackexchange.com/q/147243/2451 , physics.stackexchange.com/q/89173/2451 and links therein. –  Qmechanic Jun 19 at 21:02

1 Answer 1


\begin{equation} \boldsymbol{3}\boldsymbol{\otimes}\boldsymbol{3}\boldsymbol{\otimes}\boldsymbol{3}= \boldsymbol{1}\boldsymbol{\oplus}\boldsymbol{10}\boldsymbol{\oplus} \boldsymbol{8}^{\boldsymbol{\prime}}\boldsymbol{\oplus}\boldsymbol{8} \end{equation}

We talk about this because it explains the structure of a number of baryons in Particle Physics made from three quarks : 1 singlet - 1 decuplet - 2 octets, that is 27 baryons in total.
I refer to my answer in the following link for more details :

http://math.stackexchange.com/questions/1091189


share|improve this answer

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.