Quantum Chromodynamics

QCD enjoys two peculiar properties:

• Confinement, which means that the force between quarks does not diminish as they are separated. Because of this, when you do split the quark the energy is enough to create another quark thus creating another quark pair; they are forever bound into hadrons such as the proton and the neutron or the pion and kaon. Although analytically unproven, confinement is widely believed to be true because it explains the consistent failure of free quark searches, and it is easy to demonstrate in lattice QCD.
• Asymptotic freedom, which means that in very high-energy reactions, quarks and gluons interact very weakly creating a quark–gluon plasma. This prediction of QCD was first discovered in the early 1970s by David Politzer and by Frank Wilczek and David Gross. For this work they were awarded the 2004 Nobel Prize in Physics.

There is no known phase-transition line separating these two properties; confinement is dominant in low-energy scales but, as energy increases, asymptotic freedom becomes dominant.

There is no anlytical proof (proof with analytic continuity) of this feature. Discrete QCD can prove this.

So, if there was ever any doubt about the theory of vacuum bubbles, then this should seal the case.  The wave numbers for the two conditions are determined by the maximally packed spheres. The ratio of Nulls to Phase admit only two separable solutions.

Anyway, this is my next project. Wow, just starting gets you ten links deep into groups theory, and I eventually hit some theory Haar had, and a whole bunhc of school work comes rusing back.

But I know how this is going to end, the universal finite line counter  for sphere packers, driven from a single crank and generates quants, including their lines of symmetry. We end up with this mechanics contraption with 1,000 pencils making notches on our 3D graph, a massive minimum spanning tree of drawing tools. It will be Nlog(N) scribblers, a one hundred rank drawing tree.

Each branch of the drawing tree has a prime resolution about its radial axis, and only passes on the quant count when it counts up to its resolution.

Take on of the Boson at 47 * 2.  Put it in the center of the proton and let it make radial motion, right and left spin with 47 + 1/47 spherical modes for each wave spin motions.  I see three of those possible, 3*3*11, 11*8, 2*47, 4 * 26. Those bosons are massless because a big enough wave prime in the proton has grabbed any appropriate size that fits these bosons.  The proton, if its gluon has 13, leaves these larger wave bosons looking for 14. They try to add in the quarks, but they are 7+13, so they look for 20, and reach the edge of the orbitals, doing nothing but rounding out the sphere surface. They are limited to [2+1/2]*[47+1/47], all the other phase has better stability, the boson is its own group of two, managing a specific band of the spectrum.