Decomposing a Tensor Product of $SU(3)$ Representations in Irreps - Physics Stack Exchange most recent 30 from physics.stackexchange.com 2019-09-18T09:10:59Z https://physics.stackexchange.com/feeds/question/57607 https://creativecommons.org/licenses/by-sa/4.0/rdf https://physics.stackexchange.com/q/57607 9 Decomposing a Tensor Product of $SU(3)$ Representations in Irreps Gauge https://physics.stackexchange.com/users/8993 2013-03-21T17:11:59Z 2015-07-28T08:52:21Z <p>Can somebody explain in a simple way why, talking about representations $$3\otimes3\otimes3=1\oplus8\oplus8\oplus10~?$$</p> <p>Here $3$ and $\bar{3}$ are the fundamental and anti-fundamental of $SU(3)$, in this case. </p> https://physics.stackexchange.com/questions/57607/decomposing-a-tensor-product-of-su3-representations-in-irreps/190336#190336 1 Answer by user82794 for Decomposing a Tensor Product of $SU(3)$ Representations in Irreps user82794 https://physics.stackexchange.com/users/0 2015-06-19T20:46:04Z 2015-06-19T21:03:55Z <hr> <p>\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}</p> <p>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.<br> I refer to my answer in the following link for more details : </p> <p><a href="https://math.stackexchange.com/questions/1091189">https://math.stackexchange.com/questions/1091189</a> </p> <hr>