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But I have an issue. If this system has SU(3) symmetry, the 8 generators of SU(3) must somehow act on the various eigenstates. How exactly does this happen? Is there a book or a paper on this?

For example, the eight Gell-Mann generators of SU(3) must transform the states of the harmonic oscillator. What do they do? Do they rotate the state? How? Why are there 8 of them?

Thank you for any advice in this matter.

Cheers

François