QCD theory of the hadrons and the Yang-Mills mass gap

[Yablon]

Hello to all:

The past few months I have had little to say here. While the happy arrival of a new grandson in February and subsequent gatherings of family and friends have been partly to account, the main reason is that at the start of the 2020 I turned my attention back to four papers I published in 2012 and 2013 on why baryons are the magnetic monopoles of Yang-Mills gauge theory, and consequent phenomenological results. Specifically, it was recommended during a discussion of these papers at https://backreaction.blogspot.com/2019/ ... begin.html that I write up my proof of dynamic quark and gluon confinement, by itself, as a standalone paper, to make this research more reader-accessible. I accepted that suggestion, and on February 29, just before starting to spend the past ten days doing nothing other than being with my now-three grandsons, I completed and posted a preprint titled "QCD theory of the hadrons and filling the Yang-Mills mass gap." You may download this from:

https://www.researchgate.net/publicatio ... s_mass_gap

Those who are familiar with my tendency toward lengthy papers with lengthy sections will note that the body of this paper excluding two appendixes is only 25 pages, and that this body contains 17 sections including the introduction and conclusion. So each section on average is only about 1.5 pages long. This was done with the intention of making this paper as readable as possible, with each section focused on a single thought or step in development. So you can read a section or two at a time, go about the rest of your day or sleep on things, and then come back and read a bit more. I must credit the 4096 character limit on postings at https://backreaction.blogspot.com/ for forcing me to discipline myself into writing discrete, easily-digestible communicative segments. Also, the benefit of eight years of hindsight since I had to wrestle my way through the discoveries and writing up of my 2012-2013 papers cannot be overlooked.

Technically, section 15, which solves the Yang-Mills Mass Gap problem (https://www.claymath.org/millennium-pro ... d-mass-gap) could have been written up as a separate paper. But because all the pieces required to solve this problem and present its solution in 2.5 pages were already on the table in the rest of the paper, I decided to include that in this paper. Hence the title "QCD theory of the hadrons" (covered by sections 2-14) "and filling the Yang-Mills mass gap" (covered by section 15).

Though I did make some simplifying notation changes and explicitly include running charge strengths, and corrected what needs to be overall factor of 2/3 in the non-perturbative relation of a monopole to its fermion content (see (12.1)), the net substantive result of this paper, versus what I wrote in 2012, is unchanged. So all my subsequent phenomenological results from 2012-2013 involving nuclear binding energies, SU(8) grand unification, proton and neutron masses, etc., will be unchanged. But, the flow is much better, and I have weeded out some arguments and discussions which were unnecessary and in some instances distracting. I have also elaborated canonic versus dynamic Yang-Mills Maxwell equations, and how symmetry is broken to cause three quarks to form the backbone of an "indivisible" baryon system with massless gluons and an exact SU(3) color symmetry. These were implicitly used in my 2012 work and in the back of my mind at the time, but I never made them explicit for a critical reader. I have also emphasized the inherent recursion of Yang-Mills gauge theories, which I did not at all mention in 2012 but which I have since come to appreciate as being essential to being able to do closed, exact analytic calculations using Yang-Mills gauge theory.

So, I hope that this will provide a good, clear entree to my 2012-2013 research results, for anybody who is interested.

Best to all,

Jay

[gill1109]

Having next to no formal education as a physicist (beyond a couple of first-year Bachelor level courses which I hated because the lecturers made no attempt at all to explain what they were on about - Cambridge, UK, 1970), I would appreciate some hints of what introductory material to read in order to get some idea what this is about, and in order to be able to follow the main lines of the argument. Of course, I could start by putting a year aside in order to get hold of the 18 publications in the reference list and read some of them, but maybe the author has some better suggestions.

[Yablon]

Having next to no formal education as a physicist (beyond a couple of first-year Bachelor level courses which I hated because the lecturers made no attempt at all to explain what they were on about - Cambridge, UK, 1970), I would appreciate some hints of what introductory material to read in order to get some idea what this is about, and in order to be able to follow the main lines of the argument. Of course, I could start by putting a year aside in order to get hold of the 18 publications in the reference list and read some of them, but maybe the author has some better suggestions.

Richard, Good question.
First, you need to know Maxwell's equations in covariant form. Study section 2.5 in https://www.academia.edu/28401845/_Hans ... See.org_1_, and anything prior to that which you need.
Second, you should know about electric / magnetic duality. Study pages 88-89 of http://xdel.ru/downloads/lgbooks/Misner ... 9_PGr_.pdf.
Third, you should be comfortable with differential forms. Start with 246-248 of https://i.4pcdn.org/tg/1459871465465.pdf.
Finally, study at least sections 6.10 to 6.13 of https://ajbell.web.cern.ch/documents/eB ... eptons.pdf. And generally most of sections 4 through 6 are good background. This book has been my "bible" for 35 years.
I am happy to help if you run into specific questions along the way.
Best, Jay

[Yablon]

I just uploaded v2 of this preprint.

https://www.researchgate.net/publicatio ... ass_gap_v2

Best to all,

Jay

[FrediFizzx]

I just uploaded v2 of this preprint.

https://www.researchgate.net/publicatio ... ass_gap_v2

Best to all,

Jay

Jay, could you summarize the changes from version 1? Thanks. I'm slowly studying it.
.

[Yablon]

I just uploaded v2 of this preprint.

https://www.researchgate.net/publicatio ... ass_gap_v2

Best to all,

Jay

Jay, could you summarize the changes from version 1? Thanks. I'm slowly studying it.
.

Yes Fred, most changes were in sections 14 and 15; just cleanup elsewhere. And the main new matter regards explicitly tying the symmetry breaking to hadronization. Best, Jay