Lab Notes for a Scientific Revolution (Physics)

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.

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May 7, 2009

Inferring Electrodynamic Gauge Theory from General Coordinate Invariance

I am presently working on a paper to show how electrodynamic gauge theory can be directly connected to generally-covariant gravitational theory.  In essence, we show how there is a naturally occurring gauge parameter in gravitational gemometrodynamics which can be directly connected with the gauge parameter used in electrodynamics, while at the same time local gauge transformations acting on fermion wavefunctions may be synonymously described as general coordinate transformations acting on those same fermion wavefunctions.

This is linked below, and I will link updates as they are developed.

Inferring Electrodynamic Gauge Theory from General Coordinate Invariance

If you check out sci.physics.foundations and sci.physics.research, you will see the rather busy path which I have taken over the last month to go from baryons and confinement to studying the Heisenberg equation of motion and Ehrenfest’s theorem, to realizing that there was an issue of interest in the way that Fourier kernels behave under general coordinate transformations given that a general coordinate x^u is not itself a generally-covariant four vector.  Each step was a “drilling down” to get at underlying foundational issues, and this paper arrives at the most basic, fundamental underlying level.

Looking forward to your feedback.

Jay

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