We did not find a semiclassical model for the electron - a Feynman path integral is the way?

For the past six months we worked very hard to construct a semiclassical model for the electron. The goal was to build an intuitive model which would explain the magnetic moment and the gyromagnetic ratio of the electron.

We failed.

The magnetic moment and the spin of the electron

https://en.wikipedia.org/wiki/Dirac_equation

The magnetic moment follows quite simply from the nonrelativistic approximation of the Dirac equation. The ultimate reason for it is that the momentum operators

       p  =  i d / dx

act on the vector potential of the magnetic field, too, when we construct a solution for the Dirac equation in the nonrelativistic case under a magnetic field B.

If we take the axioms:

1. the Dirac equation describes the electron wave, and

2. the "correct" way to add a magnetic field B is to use the minimal coupling to the vector potential,

then we get the correct magnetic moment. Why is the minimal coupling the way to add a magnetic field? We do not know.

The spin of the electron follows from the Dirac equation if one guesses that the sum of the angular momentum J and the spin S should be conserved.

Using a Feynman path integral as a "particle model" of the electron

In our blog we hold the view that empty space is strictly empty of fields, except of the Higgs field. This solves the infinite energy problem of empty space (except for the Higgs field).

We would like the electron to be a particle. Then empty space is an intuitive concept: it contains no particles.

In a Feynman path integral, the electron is, in a sense, a particle. A single path can be viewed as a path of a particle.

In a path integral it is important that alternative paths of the particle must not interact. The only "interaction" allowed is the linear superposition of the end results. The probability amplitude of a final result is obtained by summing the amplitudes for each path. The weight of each path is a fuzzy concept, though.

The propagator, or the lagrangian action over a path is the probability amplitude of that path.

Conjecture. A wave equation must be linear for the Feynman path integral approach to work. We assume that the action of a path is calculated using the propagator of the wave equation.

Conclusions

We wanted to construct a semiclassical particle model for the electron, but failed.

We should determine if we can build a satisfactory particle model for the electron using the Dirac equation and a Feynman path integral.

For example, in high-energy collision experiments the electron behaves quite like a classical point particle with an electric charge. Can we explain this in an intuitive way using a Feynman path integral?