Lab Notes for a Scientific Revolution (Physics)

November 30, 2013

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

March 17, 2013

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

December 31, 2012

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:
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

June 20, 2012

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

May 24, 2012

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.

April 22, 2012

Back to Blogging, Uploaded a paper I wrote in 1986 about Preonic Grand Unification

It has been almost 3 years since my last Blog post.  Much of my time has been diverted into a condo hotel project in Longboat Key Florida, and the focus I need to do good physics has been impossible to come by.  Then, the other day, Ken Tucker, a frequent participant at sci.physics.foundations, emailed me about some new research showing that electrons have constituent substructure.  That brought me back immediately to the half a year I spent back in 1986 developing a 200-page paper about a preonic substructure for quarks and leptons, which culminated six years of study from 1980 to 1986.  I finished that paper in August 1986, and then took an 18 year hiatus from physics, resuming again in late-2004.

Ken’s email motivated me to dig out this 1986 paper which I manually typed out on an old-fashioned typewriter, scan it into electronic form, and post it here.  Links to the various sections of this paper are below.  This is the first time I have ever posted this.

Keep in mind that I wrote this in 1986.  I tend to study best by writing while I study, and in this case, what I wrote below was my “study document” for Halzen and Martin’s book “Quarks and Leptons” which had just come out in 1984 and was the first book to pull together what we now think of as modern particle physics and the (then, still fairly new) electroweak unification of Weinberg-Salam.

What is in this paper that I still to this day believe is fundamentally important, and has not been given the attention it warrants, is the isospin redundancy between (left-chiral) quarks and leptons.  This to me is an absolute indication that these particles have a substructure, so that a neutrino and an up quark both have contain the same “isospin up” preon, and an electron and a down quark both contain the same “isospin down” preon.  Section 2.11 below is the key section, if you want to cut to the chase with what I was studying some 26 years ago.  I did post about this in February 2008 at https://jayryablon.wordpress.com/2008/02/02/lab-note-4-an-interesting-left-chiral-muliplet-perhaps-indicative-of-preonic-structure-for-fermions/, though that post merely showed a 1988 summary I had assembled based on my work in 1986, at the behest of the late Nimay Mukhopadhyay, who at the time was teaching at RPI and had become a good friend and one of my early sources of encouragement.  This is the first time I am posting all of that early up-to-1986 work, in complete detail.

Lest you think me crazy, note that seventeen years later, G. Volovik, in his 2003 book “The Universe in a Helium Droplet,” took a very similar tack, see Figure 12.2 in this excerpt: Volovik Excerpt on Quark and Lepton Preonic Structure.

The other aspect of this 1986 paper that I still feel very strongly about, is taking the Dirac gamma-5 as a fifth-dimension indicator.  I know I have been critiqued by technical arguments as to why this should not be taken as a sign of a fifth dimension, but this fits seamlessly with Kaluza Klein which geometrizes the entirely of Maxwell’s theory and is still the best formal unification of classical electromagnetism and gravitation ever developed.  For those who maintain skepticism of Kaluza-Klein and ask “show me the fifth dimension,” just look to chirality which is well-established experimentally.  Why do we have to assume that this fifth dimension will directly manifest in the same way as space and time, if its effects are definitively observable in the chiral structure of fermions?  Beyond this, I remain a very strong proponent of the 5-D Space-Time-Matter Consortium, see http://astro.uwaterloo.ca/~wesson/, which regards matter itself as the most direct manifestation of a fifth physical dimension.  Right now, most folks think about 4-D spacetime plus matter.  These folks correctly think about 5-D space-time-matter, no separation.  And Kaluza-Klein, which historically predated Dirac’s gamma-5, is the underpinning of this.

After my hiatus of the past couple of years, I am going to try in the coming months to write some big-picture materials about physics, which will pull together all I have studied so far in my life.  I am thinking of doing a “Physics Time Capsule for 2100” which will try to explore in broad strokes, how I believe physics will be understood at the end of this century, about 88 years from now.

Anyway, here is my entire 1986 paper:

Preonic Grand Unification and Quantum Gravitation: Capsule Outline and Summary

Abstract and Contents

Section 1.1: Introduction

Section 1.2: Outline and Summary

Section 2.1: A Classical Spacetime Introduction to the Dirac Equation, and the Structure of Five-Dimensional Spacetime with a Chiral Dimension

Section 2.2: Particle/Antiparticle and Spin-Up/Spin-Down Degrees of Quantum Mechanical Freedom in Spacetime and Chirality, Gauge Invariance and the Dirac Wavefunction

Section 2.3: Determination and Labeling of the Spinor Eigensolutions to the Five-Dimensional Dirac Equation, and the High and Low Energy Approximations

Section 2.4: The Fifth-Dimensional Origin of Left and Right Handed Chiral Projections and the Continuity equation in Five Dimensions: Hermitian Conjugacy, Adjoint Spinors, and the Finite Operators Parity (P) and Axiality (A)

Section 2.5: Conjugate and Transposition Symmetries of the Dirac Equation in Five Dimensions, the Finite Operators for Conjugation (C) and Time Reversal (T), and Abelian Relationships Among C, P, T and A

Section 2.6: Charge Conjugation, and the Definitions and Feynman Diagrams for “Electron” and “Positron” Spinors

Section 2.7: Simple Unpolarized s,t,u Scattering Channels with a Covariant Propagator, and the Covariant (Real and Virtual) Polarization States of Massive and Massless Vector Bosons

Section 2.8: Prelude to Preons: The Spinor Decomposition of Four Real Spacetime Dimensions ct,x,y,z into Two Complex Spinor Dimensions Using the Covariant Polarization States of Vector Bosons

Section 2.9: Introduction to Isospin Preons in Electroweak Theory: The Preonic Decomposition of Four Real Electroweak Bosons A, W+, W-, Z into Two Complex Preons Denoting “Isospin Up” and “Isospin Down”

Section 2.10: Summarization of Prior Discussion, and on the Fundamental Importance of Preons in Particle Physics

Section 2.11: The Four-Preon Flavor SU(4) Unification of the Electromagnetic, Weak and Colorless Strong Interactions Excluding Quantum Gravitation; and the Colorless Flavor Classification of Left Handed Real Fermion and Boson Chiral Projections, for a Single Fermion Generation

Section 2.12: The Four-Preon Flavor SU(4)xU(1) Unification of Electromagnetic, Weak, Colorless Strong and Quantum Gravitational Interactions; and the Colorless Flavor Classification of Left and Right Handed Real Fermion and Boson Chiral Projections, for a Single Fermion Generation

Addendum to Section 2.12

Section 2.13: The Six-Preon Unification of Flavor SU(4)xU(1) with High Energy Color SU(4)xU(1) and Two Overlapping Degrees of Freedom; the Flavor and Color Classification of Real Fermions and Vector Bosons for a Single Generation; and the Derivation of Electroweak and Strong/Hyperweak Massless and Massive Neutral Current Vector Bosons

Section 2.14: On the Replication of Fermion Generations: Four Generational Grand Unification with Eighteen Preons and Nine Independent Flavor/Color/Generation Degrees of Freedom, and a Preonic Discussion of Mesons and Meson Decay

References and Bibliography

April 4, 2009

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.

December 26, 2008

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\epsilon 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\epsilon .

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

Jay.

December 11, 2008

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.

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