selfAdjoint said:
Roughly, there would be nine, but there are algebraic relations since the matrices of SU(3) are unitary. This knocks out one degree of freedom. The situation is that if you know any eight, you can solve for the ninth, so there are really only eight independent generators.
Well, this is quite vague. What is meant here is that indeed you only need eight generators in order to describe the entire symmetry group (local SU(3)-colour-symmetry). These generators really are the conserved quantity at hand, which is in this case colour. Basically this means that when particles with colour interact (like gluons and quarks and...) the total net-colour needs to be conserved (this works just like energy conservation).
A coloursinglet is a state describing a particle of which the "colour-part" cannot change when you perform colour-tranformations on it (think of these colourtransformations as rotations and they are the actual inhabitants of the SU(3)-colour-world). A particle that is a singulet is observable. So quarks on themselves are NOT observable for this reason : they carry an overall colour (R,G or B). Now watch it: a red-antired quark may seem white but it is NO coloursingulet. And being really or truly white means being a coloursinglet.
In grouptheory, you can prove that if a local symmetrygroup has dimension N, there will always be N²-1 generators that generate the transformations under which the physical quantities (like a lagrangian) need to be invariant...
But this is all math. A more physical interpretation is this one : If the wavefunction of some gluon is completely white, then there is no colour and no interaction can go on. Basically this state is a singulet which means that it can never change (no change in charge, and so on...). Now for a gluonstate to be white there is ONE condition: the particle cannot have any preference for any colour. This means that the gluon must be red-antired, green-antigreen, AND blue-antiblue.
Now incorporating some normalization-constants we have that : the
white gluon is (red-antired + blue-antiblue + green-antigreen)/sqrt(3).
For example there are two kinds of wavefunctions that are not actually white: (red-antired -green-antigreen)/sqrt(6)
and (red-antired + green-antigreen -2*blue-antiblue)/sqrt(6).
These two gluons can interact without changing
the color of a quark, but they are not completely white.Indeed, colourcharges interact via the exchange of colour. So the singlet state cannot interact because it cannot change its colours. that's why it is a singlet !Now, a red-antired gluon is indeed white BUT NO SINGLET because the colour can be changed. Indeed the total colour is white but so is the total colour of a blue-antiblue gluon so it can change into that for example. You see the difference between being white and being TRULY white ?That is the main point
An analogous things happens in the quantum information theory. Suppose you have a wavefunction that is a superposition of spin up and down. Suppose that the probability for measuring the spins along some axis is 1/2 then you really know nothing at all do you ?This same thing happens with the TRULY white wavefunction. For this reason all combinations that yield white must be included
Check out my journal for more info...
regards
marlon
ps : veel succes met de QFT-studie Dimitri...geniet ervan...
Didn't expect that...And u're saying all things about me... 
