## The Hyper-Canonical Dirac Equation

Foundations of physics and/or philosophy of physics, and in particular, posts on unresolved or controversial issues

### The Hyper-Canonical Dirac Equation

Dear Friends,

It has been several months since my last post here, but I have been spending almost all of my spare time working to perfect my Lorentz Force based paper, which can be downloaded from http://vixra.org/pdf/1710.0159v2.pdf, and is now titled:

Quantum Theory of Individual Electron and Photon Interactions: Electromagnetic Time Dilation, the Hyper-Canonical Dirac Equation, and Magnetic Moment Anomalies without Renormalization

Let me review how this differs from the last public posting of this paper in on October 15, 2017 at http://vixra.org/pdf/1710.0159v1.pdf:

1) Most importantly, I was aware at some level, but starting in late October paid close attention, to the fact that I had developed my extended version of Dirac's equation without a spin connection. If you are familiar with Dirac theory in curved spacetime, you will be aware that this is essential to proper covariance. Because the electromagnetic tetrad has the same mathematical effect as a gravitational tetrad, such a spin connection is required here too. This is developed in section 18 of the new draft at http://vixra.org/pdf/1710.0159v2.pdf. This spin connection adds some important additional terms to the extended Dirac equation, and to the Dirac Hamiltonian. In fact, because of this along with some other development (point 5 below) the full Hamiltonian with all terms takes up half a page, and one of the intermediate calculations occupies a full page. I now refer to this new Dirac equation as the "hyper-canonical" Dirac equation. This is because the usual interacting Dirac equation is the canonical result of local U(1) gauge symmetry, and this extended Dirac equation is essentially the usual equation on steroids. Most importantly: this hyper-canonical Dirac equation explains the magnetic moment anomaly without renormalization. The successful but troubling renormalization procedure -- which is needed as an ad hoc appendage because the usual Dirac equation does contain the new terms I have found here -- can and eventually will be placed into a science history museum.

2) This draft lays the foundation for calculating the hyper-canonical Dirac Hamiltonian, but does not contain that calculation. To be honest, I have spent since mid-November through the present carefully calculating out the Hamiltonian, carefully double checking all terms, and making sure nothing is missing. I am still finishing perfecting that calculation so it can be added soon.

3) Very importantly, when the entire Hamiltonian is reduced to the special case where the only external field acting on an electron is a magnetic field B, the result is exactly the same as what I found at (17.5) and in sections 18 and 19 of http://vixra.org/pdf/1710.0159v1.pdf. So those results will be added back in to today's draft, once I have high confidence in the complete Hamiltonian that I will then reduce to this special case of magnetic fields only.

4) Sections 14 and 15 of my earlier draft contain erroneous materials which are removed. Specifically, while the thought of adding the electrodynamic tetrad effects to the metric tensor and the spacetime curvature feels attractive, it comes into mathematical conflict with the earlier equations from which the hyper-canonical Dirac equation is derived.

5) Section 7 is brand new. Because of electromagnetic time dilation, the energy momentum is a function of spacetime, and its gradient contains the electric field E and the time derivative of the three-potential A. This result is important for later use when we engage in some commutations to produce the Hamiltonian, and is the source of the electric fields which I now have in the Hamiltonian that I am still fitting with finishing touches before I put it out in public.

6) In order to properly calculate the complete Hamiltonian, it is important to carefully develop the mathematical and physical properties of individual photons. And, it is important to understand the gauge theory relation between a classical (c) external potential $A_c^\mu$ and an individual photon ($\gamma$) potential $A_\gamma^\mu$. That is the purpose of sections 15 which has a great deal of new material, and section 16 which is brand new, just finished this yesterday morning.

7) While I have not made any final decision, my inclination at this time, once the new Hamiltonian is ready, is to restore the Hamiltonian to the paper, show the reduction to when there are only B fields, essentially restore previous sections 17, 18 and 19 from http://vixra.org/pdf/1710.0159v1.pdf to show the magnetic moment anomaly without renormalization, and be done with this paper. Studying the Hamiltonian under varying sets of other conditions -- electric fields, external potentials, external source and current densities, angles of interaction between the fermion and photon (interaction angle was discussed in v1) -- would go into a separate, subsequent paper. There will be many opportunities for experimental validation, because the Hamiltonian will allow a "user" to pick all of the external conditions in varying combinations, and determine what energies should be observed under any choice or combination of experimentally-controllable conditions.

I always appreciate good feedback, and am happy to answer any questions.

Thanks,

Jay
Yablon
Independent Physics Researcher

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