The Yang-Mills Mass Gap Solution

Friends,

I have been a bit behind with this blog, but wanted to let you know that I have pulled together many of the various threads I have posted over the past several years into a complete solution to the Yang-Mills and Mass Gap Problem, which paper is here:

The Yang-Mills Mass Gap Solution.

The Mass Gap problem was specified back in 2000 by Arthur Jaffe and Edward Witten at

http://www.claymath.org/millennium/Yang-Mills_Theory

This problem really has four aspects, which are as follows: 1) the mass gap itself, 2) QCD confinement, 3) chiral symmetry breaking and 4)  proof of the existence of a relativistic quantum Yang-Mills field theory in four-dimensional spacetime.  Each of these is respectively presented in sections 10, 11, 12 and 13 of this paper.

You can read the paper abstract, so I will not repeat it here.  But I will also be delivering an oral presentation of this work at the April 2014 APS meeting in Savannah, Georgia.  Yesterday, I submitted the abstract for that presentation, which is below:

APS Abstract: The Yang-Mills Mass Gap problem is solved by deriving SU(3)_C Chromodynamics as a corollary theory from Yang-Mills gauge theory.  The mass gap is filled from the finite non-zero eigenvalues of a configuration space inverse perturbative tensor containing vacuum excitations.  This results from carefully developing six equivalent views of Yang-Mills gauge theory as having: 1) non-commuting (non-Abelian) gauge fields; 2) gauge fields with non-linear self-interactions; 3) a “steroidal” minimal coupling; 4) perturbations; 5) curvature in the gauge space of connections; and 6) gauge fields related to their source currents through an infinite recursive nesting.  Based on combining the Yang-Mills electric and magnetic source field equations into a single equation, confinement results from showing how the magnetic monopoles of Yang-Mills gauge theory exhibit color confinement and meson flow and have all the required color symmetries of baryons, from which we conclude that they are one and the same as baryons.  Chiral symmetry breaking results from the recursive behavior of these monopoles coupled with a view of the Dirac gamma matrices as Hamiltonian quaternions extended into spacetime.  Finally, with the aid of the “steroidal” view, the recursive view of Yang-Mills enables polynomial gauge field terms in the Yang-Mills action to be stripped out and replaced by polynomial source current terms prior to path integration.  This enables an exact analytical calculation of a non-linear path integral using a closed recursive kernel and yields a non-linear quantum amplitude also with a closed recursive kernel, thus proving the existence of a non-trivial relativistic quantum Yang–Mills field theory on R⁴ for any simple gauge group G.

I am of course interested in any comments you may have.

Jay

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My four recent peer-reviewed papers about Magnetic Monopole Baryons are now all published and online

I wanted to let you know that my recent second, third and fourth peer-reviewed papers were all published on April 30.  These papers, in order of logical development, are:

2)  J. Yablon, “Predicting the Binding Energies of the 1s Nuclides with High Precision, Based on Baryons which Are Yang-Mills Magnetic Monopoles,” Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 70-93. doi: 10.4236/jmp.2013.44A010.

Link: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=30817

3)  J. Yablon, “Grand Unified SU(8) Gauge Theory Based on Baryons which Are Yang-Mills Magnetic Monopoles,” Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 94-120. doi: 10.4236/jmp.2013.44A011.

Link: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=30822

4)  J. Yablon, “Predicting the Neutron and Proton Masses Based on Baryons which Are Yang-Mills Magnetic Monopoles and Koide Mass Triplets,” Journal of Modern Physics, Vol. 4 No. 4A, 2013, pp. 127-150. doi: 10.4236/jmp.2013.44A013.

Link: http://www.scirp.org/journal/PaperInformation.aspx?PaperID=30830

The “Special issue on High Energy Physics” in which the foregoing all appear is at: http://www.scirp.org/journal/jmp/

Also, the very first paper in which is is all rooted was published a couple of months ago, but finally went online about ten days ago.  This paper may be downloaded at:

1)  Yablon, J. R., Why Baryons Are Yang-Mills Magnetic Monopoles, Hadronic Journal, Volume 35, Number 4, 401-468 (2012)

Link: http://www.hadronicpress.com/issues/HJ/VOL35/HJ-35-4.pdf

If you want to quickly understand the original paper #1, which is 67 pages, I suggest that you start by reading the introductory section in paper #2, which is a three page encapsulation of paper #1.  Overall, this introductory section of paper #2 is the best point entry to understanding my recent research.  I am happy to answer questions or engage in discussions online.

Best to all,

Jay

My first published paper “Why Baryons Are Yang-Mills Magnetic Monopoles” at Hadronic Journal, Volume 35, Number 4, 399-467 (2012)

My first paper “Why Baryons Are Yang-Mills Magnetic Monopoles” has now been published in Hadronic Journal, Volume 35, Number 4, 399-467 (2012). Though the Hadronic Journal has not yet put this issue online, I have a hardcopy of this and have uploaded a scan at the link below:

Hadronic Journal, Volume 35, Number 4, 399-467 (2012)

As I have advised on some earlier blog entries, I have two more accepted papers which will be published next month (April 2013) in the Journal of Modern Physics, Special Issue on High Energy Physics.

Jay

New Paper: Predicting the Binding Energies of the 1s Nuclides with High Precision, Based on Baryons which are Yang-Mills Magnetic Monopoles

Dear Friends:

I wanted to let you all know that I just posted a new paper, which you can review at the link below:

http://vixra.org/abs/1212.0165

The abstract is as follows:

We employ the thesis that baryons are Yang-Mills magnetic monopoles to predict the binding energies of the alpha ⁴He nucleus to less than four parts in one million, of the ³He helion nucleus to less than four parts in 100,000, and of the ³H triton nucleus to less than seven parts in one million, all in AMU.  Of special import, we exactly relate the neutron–proton mass difference – which pervades all aspects of nuclear physics and beta decay – to a function of the up quark, down quark, and electron masses, which in turn enables us to predict the binding energy for the ²H deuteron nucleus most precisely of all, to just over 8 parts in ten million.  The thesis that Baryons are Yang-Mills magnetic monopoles thereby appears to have ample, indeed irrefutable empirical confirmation, establishes a basis for finally “decoding” the mass of known data regarding nuclear masses and binding energies, and may lay the foundation for technologically realizing the theoretical promise of nuclear fusion.

I have also submitted this for journal publication, and hope that this will become my second journal-published paper.  The first one as I have advised previously has already been accepted and will be released any day now.

I welcome your comments, as always.

Time to go party!  Happy new year to all!

Jay

Accepted for Publication: Why Baryons Are Yang-Mills Magnetic Monopoles!

I am very pleased to report that the paper linked below, “Why Baryons Are Yang-Mills Magnetic Monopoles,” has been accepted for publication in Number 4, Volume 35, 2012 pp 401-468 of the Hadronic Journal.  This is due to be released in early January, 2013.

Why Baryons Are Yang-Mills Magnetic Monopoles Final for Publication

As you can see from elsewhere in this blog and in my various newsgroup posts, I have been advocating since 2005, the view that protons and neutrons and other baryons are Yang-Mills magnetic monopoles.  In this paper, I have finally developed the empirical proof, by predicting nuclear binding energies between such monopoles which accord with empirical binding data within a fraction of a percent, and by explaining how the nuclear binding energies relate to the energies which confine quarks within their respective nucleons.

If you want to start somewhere other than at the beginning, go to page 61 where you will see how I derive the up and down quark masses to six digit in MeV accuracy based on the electron rest mass and the deuteron binding energy, and where I show a predicted maximum available binding energy for ^56Fe of 493.028394 MeV.  The empirical data show that this nucleus has an empirical binding energy of 492.253892 MeV, which means that ^56Fe utilizes 99.8429093% of the energy predicted to be available, for actual binding.  The remaining 0.16% is used to continue to confine quarks within the nucleons that comprise ^56Fe, and this utilization of available binding energy is the maximum among all of the known nuclei, and sets the boundary between fusion and fission physics.

I believe that this will become big news as this work gains exposure and people begin to see what problems have been solved here.

Happy holidays to all!

Jay