elas said:
Thanks, I think I have enough to start making progress again. Its always easy for those who know the answers!
elas
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 (invariant under colour-rotations). 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 thing 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
marlon