Just because the SU(3) force is a perfect symmetry doesn’t mean that the particles that suffer it are perfect SU(3) particles. They have other quantum numbers and forces that are not SU(3) symmetric and those other forces contribute to bound states.

I submitted the paper to Phys Math Central. The referees did not complain about the potential. They complained that the paper wasn’t connected to the other results known on quarks and consequently wouldn’t be an advance in the field. So I decided to write another paper that would more directly tie in with what was known. That is Spin Path Integrals and Generations, which was submitted to Foundations of Physics earlier this month and is now in review.

In particle physics, one often finds that there are multiple ways of looking at something that seem to be entirely unrelated but actually have deep connections. What I am doing is of this nature. Instead of examining things from the point of view of position and momentum I’m looking at the particles as if the interaction occurred at only a single point. This gives an approximation that is dual to the usual one. They’re related approximations, but not as one being an improvement to the accuracy of the other.

The usual approx. is most accurate for heavy quarks at low energies. Mine is most accurate for energetic light quarks. But from the referee reports I didn’t see how I could argue this with them. All they wanted to talk about was how quarks are modeled using the usual ways. I decided that I needed to put a more fundamental paper in the literature showing that this was a natural thing to do, hence the FoP paper.

Difficulty in publishing is natural for ground breaking papers. There are plenty of examples. I’ve barely started to try to get this published.

Did you end up submitting the paper? What did the referees’ reports say?

The “color matrix” V is an abbreviation for a lot of complicated stuff. For an example of this, see the first equation on page (4) of Statistical Mechanics of semi-classical colored Objects Phys.Lett. B478 (2000) 161-171.

In their paper, they’re interested in the interaction energy between quarks and so they pay attention only to the alpha and beta indices. My model is keeping track of the beta and beta’ indices only, that is, just one of the quarks. This is in analogy to how you model a 2-body interaction by keeping track of the difference between positions of the two bodies, rather than both sets of individual positions. If you know that the color of one quark is “red”, then by color neutrality you know that the color of the other quark, plus free gluons, is “anti-red”.

Their paper assumes a simple interaction with a single gluon, so they don’t have as many arbitrary parameters and can evaluate the color matrix from perturbation theory. See their table on top of page 4. But I’m interested in the exact non perturbational theory (which cannot be calculated) so I have to assume a more arbitrary potential.

But even an arbitrary interaction needs to be assembled from stuff that treats the three possible quark colors equally. That’s not a general symmetry of SU(3) perturbation theory; it’s a symmetry of the three states in the “3″ irrep of SU(3). It’s a statement about how very complicated non perturbational amplitudes must depend on color.

But these transformations, for U in SU(3), don’t preserve the “one-circulant” property of V which you claim is required.

Instead, the matrix is for the interaction between three colored particles. Its eigenvectors correspond to different ways of mixing colored quarks. The three solutions all have equal amplitudes and so the three solutions each correspond to one red quark, one green, and one blue. This is neutral in color, which is okay.

M_leptons * c / 2pi = 1.6017399 E-019 = e_lep

e_lep /elem. chg = .999728

If this is more than a coincidence, that means charge has dimensions of momentum.