Yang-Mills Mass Gap

My study of vector field twists has led to the discovery of stable continuous field entities as described in the previous post (Dec 29th A Particle Zoo!).  I’ve categorized the available types of closed and open solutions into three broad groups, linear, knots, and links.  There’s also the set of linked knots as a composite solution set.  I am now trying to write a specialized simulator that will attempt quantitative characterization of these solutions–a tough problem requiring integration over a curve for each point in the curve–even though the topology has to be stable (up to an energy trigger point where the particle is annhiliated), there’s a lot of degrees of freedom and the LaGrange methodology for these cases appears to be far too complex to offer analytic resolution.  While the underlying basis and geometry is significantly different, the problem of analysis should be identical to the various string theory proposals that have been around for a while.  The difference primarily comes from working in R3+T rather that the multiple new dimensions postulated in string theory.  In addition, string theory attempts to reconcile with gravity, whereas the field twist theory is just trying to create an underlying geometry for QFT.

One thing that I have come across in my reading recently is the inclusion of the mass gap problem in one of the seven millenial problems.  This experimentally verified issue, in my words, is the discovery of an energy gap in the strong force interaction in quark compositions.  There is no known basis for the non-linear separation energy behavior between bound quarks or between quark sets (protons and neutrons in a nucleus).  Dramatically unlike central quadratic fields such as electromagnetic and gravitational fields, this force is non-existent up to a limit point, and then asymptotically grows, enforcing the bound quark state.  As far as we know, this means free quarks cannot exist.  As I mentioned, the observation of this behavior in the strong force is labeled the Yang-Mills Mass Gap, since the energy delta shows up as a mass quantization.

As I categorized the available stable twist configurations in the twist field theory, it was an easy conclusion to think that the mass gap could readily be modelled by the group of solutions I call links.  For example, the simplest configuration in this group is two linked rings.  If each of these were models of a quark, I can readily imaging being able to apply translational or moment forces to one of the rings relative to the other with nearly no work done, no energy expended.  But as soon as the ring twist nears the other ring twist, the repulsion factor (see previous post) would escalate to the energy of the particle, and that state would acquire a potential energy to revert.  This potential energy would become a component of the measurable mass of the quark.

The other question that needs to be addressed is why are some particles timewise stable and others not, and what makes the difference.  The difference between the knot solutions and the link solutions is actually somewhat minor since topologically knots are the one-twist degenerate case of links.  However, the moment of the knot cases is fairly complex and I can imagine the energy of the configuration could approach the particle energy and thus self-destruct.  The linear cases (eg, photons, possibly neutrinos as a three way linear braid) have no path to self destruct to, nor does the various ring cases (electron/positrons, quark compositions).  All the remaining cases have entwining configurations that should have substantial moment energies that likely would exceed the twist energy (rate of twisting in time) and break apart after varying amounts of time.

The other interesting realization is the fact that some of these knot combinations could have symmetry violations and might provide a geometrical understanding of parity and chirality.

One thing is for sure–the current understanding I have of the twist field theory has opened up a vast vein of potentially interesting hypothetical particle models that may translate to a better understanding of real-world particle infrastructure.


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