I am reading quark model. I don't understand what's the meaning of a color $SU(3)$ or $SU(3)_c$ group and how it differs from a general $SU(3)$ group. Please elaborate.
$\begingroup$
$\endgroup$
2
-
$\begingroup$ Reading where? Which page? $\endgroup$– Qmechanic ♦Commented Dec 8, 2023 at 15:43
-
1$\begingroup$ I don't think my question requires that information. $\endgroup$– Sagar K. BiswalCommented Dec 8, 2023 at 15:54
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
1
They are mathematically the same group (i.e they are isomorphic) but physically different. The colour group acts only on the colour degrees of freedom while the the orginal Gell-Man-Ne'eman flavour group acts on the $u,d,s$ flavours. You can think of the quarks (in the case of three flavours only) having two sets of indices $q_{ij}$ where the $q_{1j}=u_j$ $q_{2j}=d_j$, $q_{3j}=s_j$, where the $j$ index, taking values 1,2,3, lables the colour which couples to the gauge fields.
answered Dec 8, 2023 at 15:28
-
$\begingroup$ Thank you. I understand it completely now. $\endgroup$ Commented Dec 8, 2023 at 16:01
$\begingroup$
$\endgroup$
1
The $c$ subscript merely denotes what property the group acts on. If the particles transform under multiple groups this will help clarify the structure. For instance the up and down quarks transform between each other under "isospin" which is $SU(2)$, but they also transform under color which is $SU(3)$. To clarify you could say that a quark multiplet is in the fundamental representation of $SU(2)_I\times SU(3)_c$.
-
$\begingroup$ Thank you for the insight. $\endgroup$ Commented Dec 8, 2023 at 16:01