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"We can now see how a supermultiplet of ten baryons may arise. Baryons are made of three identical fermions, so the possible states may be classified according to their symmetry under interchange of quark labels. Altogether there are 27 states. One of these is totally anti-symmetric: uds+dsu+sud-usd-sdu-dus,

and ten symmetric states:

uuu,

ddd,

sss,

uud+udu+duu,

uus+usu+suu,

udd+ddu+dud,

uss+ssu+sus,

dds+dsd+sdd,

dss+ssd+sds,

uds+dsu+sud+usd+sdu+dus"

I am a little bit lost here, first question:

what is a supermultiplet...? Also, what does he mean by interchange of quark labels?

second question:

How are these states supposed to clearly follow from the existence of 27 states...? I'm not really sure how I'd come up with these states.

For "uud+udu+duu"

(assuming I'm not missing something really obvious) my first thought was "2 up quarks, 1 down...proton"? I feel like I'm missing something obvious here, besides the idea that the terms don't commute (which I'm guessing is part of this). Wait, it said these were non-normalized...normalized would we have 1/sqrt 3(uud+udu+duu) and then the whole thing would just be the different states of a proton? I feel like I'm seriously over simplifying at this point.

Thanks for any and all help,

Elwin

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# Quark Model (Supermultiplet and States questions)

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