As I said last week I have started developing a paper that will incorporate the review I received from PRD for the Yang-Mills monopole paper, and fundamentally, the thesis will migrate over to "Why SU(3)_C t’Hooft Polyakov Monopoles are baryons." The ultimate results will be the same; but the connections to the scalar fields will be much more explicitly developed.

The other night I was getting a start on the first section of this paper, which was intended to be a "review" of Dirac Monopoles and the Dirac Quantization Condition without strings, using the gauge field method pioneered by Wu and Yang, which Zee reviews very nicely at https://jayryablon.files.wordpress.com/ ... opoles.pdf. This was to serve as an introduction to t'Hoot-Polyakov monopoles, and to rebut point 3 of the PRD review of the classical side of the theory, which as I shared last week was the following:

PRD Chief Editor wrote:3) The surface integral of F is not gauge-invariant, and neither are the other surface integrals of quantities that you write down. By appropriate local gauge transformation any nonzero surface integral of F can be made to vanish. This not only invalidates your Eq. (3.3), but shows that physical conclusions cannot be drawn from the value of this quantity.

In the process of doing this development, it occurred to me that certain solutions of the Dirac monopole had never been fully developed, and as I explored those states which had been "left on the table" by others, I began to realize that this could be used to account fully and completely for the fractionalized charge pattern observed in the Fractional Quantum Hall Effect. So over the weekend I wrote up an 11 page paper you may review at http://vixra.org/pdf/1411.0552v1.pdf, which as of Thursday I had no anticipation of writing. I do not think of myself as a condensed matter theorist, so I felt a bit like a fish out of water, but managed to do enough review of this area and got some private comments from a friend who is a professional condensed matter theorist, all of which made me comfortable I was not too badly off any bases. I also submitted this paper to PRD, and will let you know what happens.

Here is the Abstract:

The purpose of this paper is to explain the pattern of fill factors observed in the Fractional Quantum Hall Effect (FQHE), which appears to be restricted to odd-integer denominators as well as the sole even-integer denominator of 2. The method is to use the mathematics of gauge theory to develop Dirac monopoles without strings as originally taught by Wu and Yang, while accounting for orientation / entanglement relationships between spinors and their environment in the physical space of spacetime. We find that the odd-integer denominators are included and the even-integer denominators are excluded if we regard two fermions as equivalent only if both their orientation and their entanglement are the same, i.e., only if they are separated by 4π not 2π. We also find that the even integer denominator of 2 is permitted because unit charges can pair into boson states which do not have the same entanglement considerations as fermions, and that all other even-integer denominators are excluded because only integer charges, and not fractional charges, can be so-paired. We conclude that the observed FQHE fill factor pattern can be fundamentally explained using nothing other than the mathematics of gauge theory in view of how orientation / entanglement applies to fermions but not to bosons, while restricting all but unfractionalized fermions from pairing into bosons.

Best to all,

Jay