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

Slides from my first Physics Lecture, and a New Draft Paper Summarizing the Experimental Points of Contact which Affirm my Work

This past week I gave my first physics lecture on the research in my recent four published papers establishing that proton and neutrons are actually a particular type of magnetic monopole (based on a theory called Yang-Mills because those are the names of the two fellows who invented its foundations).  In the lecture, I consolidated all four of my papers totaling about 140 pages into a 70 minute lecture (50 minutes talk, 20 minutes Q&A discussion) and 64 slides which you can download from Physics Lecture Slides.

It would probably take someone a couple of weeks to read through and thoroughly understand my four papers.   The slides were designed to allow someone to assimilate the same information within a couple of hours.  Please take a look.

Also, I prepared a new paper which you may read at Fitting the 2H, 3H, 3He, 4H Binding Energies 3  which in ten pages lays out the multiple relationships I have found which very clearly connect to experimental data that had never before been explained.  This is the “tip of the iceberg” in terms of the multiple ways in which nature herself validates my theoretical work at the parts-per-million level.   My hope is that people in the physics community will see these results, realize that there is something real here, and then take the time to backtrack to understand the theoretical foundations that got me to that point.  A sort of “inversion” of my work to lead with the experimental results in order to catalyze interest.  Everything in this paper by the way, is simple arithmetic (as in, numbers calculated and compared to other numbers), and about the only complexity is that you need to understand a tiny bit about matrix multiplication (like that the “Trace” of a square matrix is just the sum of all the entries long its upper left to lower right diagonal).  If you do not want to even sort through the matrix stuff, then just look at equations (14) through (20).  These are pure numbers, and you will see how close I get to the experimental data each and every time.  Nobody has ever before explained this experimental data with such high precision!

People, I am usually careful not to toot too loudly about my work.  But I have to say that this is real, it is fundamental, and it will revolutionize nuclear and particle theory.  The question is no longer if, but when.  The discoveries have been made and they are in print and all they need is attention from the right places.  My “lab notes” and related work will soon spark a “scientific revolution” toward which I have been working for over 40 years.  Real results in hand, I am now doing all that I can to make that happen sooner rather than later.  I welcome any help or support my friends can provide in making that happen.

Jay

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

Might Baryons be Yang-Mills Magnetic Monopoles?

If you have followed my blog the past few years or been a participant sci.physics.foundations, you will know that since early 2007 I have been advocating that baryons are Yang-Mills magnetic monopoles, hiding in plain sight.   Now, finally, I have developed rigorous mathematical proof of this, and it is in a paper you may read at:

2012 Baryon Paper Final

The equation which encapsulates the entire thesis, is (8.1), and I have copied it below into this post.  Now you can read the paper, see how I got to (8.1), and understand exactly what this equation is saying about nuclear physics.

Jay

Baryons and Confinement; Exact Quantum Yang Mills Propagators; Mass Gap

To all:

I have started work on physics again this last month after two years “sabbatical.”  I am also again working with my friend Andrej Inopin.

In particular, I am touching up a paper that I was working on in 2008 which shows that baryons are simply magnetic charges in a non-Abelian (Yang Mills) gauge theory, and shows how confinement phenomena are a natural outgrowth of the properties of these “magnetic charge baryons.”  This paper is linked at:

https://jayryablon.files.wordpress.com/2012/05/baryon-paper-3-1.pdf

Now, in returning to this paper after several years, I have always known that my equation (3.5) in the above was a “shortcut” to get to the results  afterwards, because it relies upon an analogy from QED and does not fully develop propagators / inverses for Yang-Mills theory.

This is because back in 2008, I did not know how to quantize Yang-Mill theory and obtain exact propagators that embody all of the non-linearity that comes from Yang-Mills.  Nobody knew / knows how to do this.  That is why people still use perturbation theory even though it breaks up the gauge invariance of Yang-Mills, or use lattice gauge theory even though it breaks up Lorentz symmetry and they have to calculate numerically on computers rather than analytically.  These are “compromises” that everybody uses because exact Yang-Mills quantization solutions simply are not known to date.

But in the last several weeks, I returned to this problem that had been a roadblock for me in 2008, and have now solved it!   The link below is the current version of a paper I have written in the last two weeks which contains this solution.

https://jayryablon.files.wordpress.com/2012/05/quantum-yang-mills-3-for-spf.pdf

Sections 2 and 3 in the above just link replace the “shortcut” of (3.5) in the previous link further up this page.  Section 4 shows that the perturbation which is an important object in this theory actually transforms just like a GRAVITATIONAL field.  I write this with the view that this is a possible path to non-Abelian quantum gravity, but am reserving judgment on this and would like to hear other views.  But what I think is unmistakable is that this shows that gauge transformations in the perturbation — which might be reason to doubt using this perturbation to calculate invariant numbers — are equivalent to no more and no less that plain old general coordinate transformations.  In essence, the perturbation combines several dot products which alone are not invariant, but which together, are.

The work in this paper lays the foundation and provides the calculating machinery for solving the “mass gap” problem.  I will continue developing this in the week ahead, but I have enough already that I wanted to share.

Starting a new paper on Baryons and Confinement

Today, I began work on a new paper dealing with the Yang-Mills foundations of baryons and QCD confinement.  The first draft is linked below, and I will provide updates as they develop.

Yang-Mills Foundations of Baryons and Confinement Phenomena

I may get diverted a bit by my US tax filing the next few days, and I am quite busy at work right now so this will mostly be a weekend and after-midnight project, but I do hope to get this paper, which I hope will synthesize many individual insights I have had and subjects I have studied over the past several years, into a something of value for others.

Constructive comments are always appreciated.

Thanks to the Princess and Peter and Ken and Igor and Ben for feedback and insights posted on the various newsgroups.

Jay.

S=2, mu=0 Meson Mass Spectrum, and some interesting possible ties to experimental meson data

Before I head out on holiday, I also wanted to post one more item:

In equation (11.8) of my earlier post at:

https://jayryablon.files.wordpress.com/2008/12/su-3-paper-20.pdf

I showed the matrix inverse for mesons based on the values of S=2 and mu=0 using the parameters of the theory developed in that work (which is based on the post I made a few hours ago).

I finished a detailed calculation of the predicted meson masses as a fraction of “.5vg” and put them in ascending order, in the following one-page listing:

https://jayryablon.files.wordpress.com/2008/12/s2-mu0-mass-spectrum.pdf

This is the type of theoretical result that we need to try to fit to experimental meson masses.  That is, this is where the “rubber meets the road.”

In this regard, I point that there are good reasons from the underlying theory to compare and take the ratios of numbers in the above with the 1+/-i factors, and to consider the SU(3) vector to be (uds) from the old quark flavor models (as opposed to the (RGB) of color).

One of these ratios is that of what is the 4,5 mass matrix element to the 1,2 element:

 .625727090299/.169470755895=3.69220577135

and this should be related to the ratio of the meson K^0=d s-bar to pi^0=d d-bar.  That experimental ratio is, in fact:

K^0/pi^0 = 497.614 MeV / 134.9766 MeV = 3.6867

This is *very* close (they differ by 1.5 parts per thousand!), and could be an experimental validation of the whole theory, since the only thing not accounted for theoretically are QED corrections!

Another ratio of interest is:

 .169470755895/.163577444819=1.03602765089

This is because the experimental pi^+/- to pi^0 ratio is:

 pi^+/- / pi^0 = 139.5701 MeV / 134.9766 MeV = 1.0340

This also is rather tantalizing, and is off by just under 2 parts per thousand!

Still trying to figure out the whole fit, but I’ll leave you all with that for now.

Happy new year!

Jay.

Finite Amplitudes Without +i\epsilon

To all,

I have now completed a paper at the link below, which summarizes the work I have been doing for the past two months (and in a deeper sense, for much of my adult life) to lay a foundation for understanding and calculating particle masses:

finite-amplitudes-without-i-epsilon

I have also taken the plunge and submitted this for peer review. ;-)?

The abstract is as follows:

By carefully reviewing how the invariant amplitude M is arrived at in the simplest Yang-Mills gauge group SU(2), we show how to arrive at a finite, pole-free amplitudes without having to resort to the “+i prescription.”  We first review how gauge boson mass is generated in the SU(2) action via spontaneous symmetry breaking in the standard model, and then carefully consider the formation of finite, on-shell amplitudes, without +i.

Comments are welcome, and I wish everyone a happy holiday and New Year!

Jay.

Understanding the QCD Meson Mass Spectrum

Dear Friends:

It has been awhile since I last posted and it is good to be back.

Almost two years ago in the course of my work on Yang Mills, I came across what I believe is an approach by which mass spectrum of the massive mesons of QCD might be understood.  I had what I still believe is the right concept, and many of the pieces, but I could not figure out the right execution of the concept in complete detail.  Over the past year and a half I walked away from this to let the dust settle and to also arrive at a place where the basic principles of quantum field theory were no longer “new” to me but had become somewhat ingrained.  Now, I believe I have found the right way to execute this concept, and the results are intriguing.

In the file linked below, which I will update on a regular basis in the coming days:

https://jayryablon.files.wordpress.com/2008/12/su-3-paper-20.pdf,

 I review how mass is known to be generated in SU(2), as a template for considering SU(3) QCD.  I have tried to explain as simply as possible, what I believe to be the origin of QCD meson masses, as well as to lay the foundation for theoretically predicting these.  Keep in mind, finding out how the vector mesons of QCD obtain their non-zero masses, which make the QCD interaction short range despite supposedly-massless gluons, is one aspect of the so-called “mass gap” problem, see point 1) on page 3 of
http://www.claymath.org/millennium/Yang-Mills_Theory/yangmills.pdf at
http://www.claymath.org/millennium/Yang-Mills_Theory/.

Then, I extend this development, in detail, to SU(3).

Several interesting results are already here:

1)  This approach neatly solves the problem of propagator poles (infinities) in a manner which I believe has not heretofore been discovered.  Goodbye to the +i\eta prescription, off mass-shell particles, and other inelegant dodges to achieve a finite propagator.

2) This approach may solve the confinement and the mass gap problems simultaneously.  It is important to understand that electroweak SU(2)xU(1) is a special case in which the gauge bosons are synonymous with the observed vector mesons, but that in SU(3) and higher order theories they are not.  The gauge bosons aka gluons, which show up in the Lagrangian, are not observed.  What is observed are the vector mesons which pass through to the denominator of the propagator in the invariant amplitude.

3) There emerges is a quantum number that is restricted to three discrete values, and depending on which value of chosen, all the meson masses are scaled up or down on a wholesale basis.  I believe that this may resolve the problem of generation replication.

I expect to be churning out mass calculations in the next day or two.  You may wish to check out the meson mass tables at http://pdg.lbl.gov/2008/tables/rpp2008-qtab-mesons.pdf, because that table contains the data which I am going to try to fit to equation (6.1), via (6.5).

Hope you enjoy!

Jay.