The introduction of color and it's antisymmetric wavefunction.

[center o bass]

I've read that color was introduces as a degree of freedom nessecary to satisfy the pauli exclusion principle in the quark model of particles. For example for the omega minus which had an observed total spin of 3/2 and no angular momenta ment that the spin had to the the same for all of the three quarks. The argument that I'm not sure about is the argument that the quarks is in the same spatial possition and thus we have to introduce a new degree of freedom which must be antisymmetric under the exchange of the quarks.

The quarks of a baryon is confined within about 10^{-15}, now this is a small space, but it contains infinitely many points, so the way i see it, it should be perfectly allowable for the quarks to that make up the particle to be in different spatial positions. Does anyone have an explenation for this?

I guess I could see that IF the quarks were at the same position, the whole baryon would pop out of excistence since the wf would then be nil, but as the quarks moved about it would shortly reappear and within the framework of quantum mechanics I don't see a problem with that. Thanks for any help in clarifying this.

 

[Bill_K]

The quarks are not "in the same position", but for the omega minus as well as for the other lowest lying hadrons, they are in the ground state. This means the spatial wavefunction is totally symmetric, an S-wave with L = 0.

Similarly. in a hydrogen atom, if the electron is in the ground state, it's an S-wave, but that doesn't mean it's in the same position as the proton!