# Different representations of SU3 and resultant multiplets

1. Apr 12, 2010

### metroplex021

I have a very basic query about multiplets. In the SU(3) approach strongly interacting particles, quarks and hadrons are the basis vectors of irreducible representations of SU(3). Now, quarks and hadrons are definite properties with define eigenvalues of hypercharge and isospin: to put it another way, there is only one set of quarks and hadrons. But there are many different irreducible representations of SU(3). For example, we are free to choose the Cartan representation, or the Gell-Mann representation, of the SU(3) matrices as our representation of SU(3). How do we know that these different representations will all produce particles with the same set of eigenvalues of isospin and hypercharge - ie, how do we know whatever representation we choose, we'll get back our actual quarks and the hadrons? Any help would be appreciated. Thanks!

Last edited: Apr 12, 2010
2. Apr 13, 2010

### seggahme

quarks and hadrons are NOT the basis vectors.

3. Apr 13, 2010

### metroplex021

Really? But Lichtenberg for example in 'Unitary Symmetry and Elementary Particles' (p34) writes "The basis vectors of an irreducible unitary representation of a symmetry transformation denote a set of quantum mechanical states. These states are said to constitute a multiplet." The three quarks, and the baryon octet etc, all constitute multiplets. So why is it they're not basis vectors? -- Thanks a lot.

4. Apr 14, 2010

### jeblack3

If flavor SU(3) was a perfect symmetry of the world, then all of the baryons in the baryon octet would be indistinguishable. They would all have the same mass, charge, etc. But it isn't. It's broken by the mass and charge differences of the up, down and strange quarks. It's these symmetry-breaking effects that pick out which components of an SU(3) multiplet correspond to observed baryons.