The charge of the electron is positive - its field is negative

We have the model where the electron is a small weight resting on a drum skin. It makes a pit into the skin. The pit is the static electric field (more precisely, its potential) of the electron.

The electric charge of the electron is positive

The hamiltonian contains the energy of the static electric field of the electron, as well as the potential of the positive charge of the electron in the potential pit of the electric field. The hamiltonian will get a smaller value if we make a potential pit into the electric field, and put the electron in that pit.

Yes, the electric charge of the electron is positive. That is why it creates a field which from the outside looks like the field of a negative charge.

If the electron would be a classical point particle, it would sink deeper and deeper in the electric potential. It would release an infinite amount of energy, and the energy of the field would become infinite, too.

       ---------          --------  electric potential

                   \ ●/ 

                     electron in potential pit

We conclude that a classical point charge cannot exist. We believe that zitterbewegung is the mechanism which rescues the quantum mechanical electron from the infinite negative potential.

Why is the electron mass 511 keV? Maybe it is just a random value. The muon mass is 105.7 MeV, which looks like a random value, too.

In the drum skin model, it is the small weight which creates the pit. Having a weight pressing the skin is equivalent to having a small hammer hitting the skin at the location of the electron with a very high frequency.

In the hammer model, the drum skin responds to each hit with a Green's function. It is the impulse response.

The spectrum of the Green's function behaves like this:

1. High frequencies are "reflected" back to the hammer quickly and the hammer absorbs them.

2. Low frequencies are reflected back slower. There is a buildup of low frequencies from many hits of the hammer in the skin.

We may imagine that the 1 / r² electric field of the electron is "built" from these frequencies.

The Feynman diagram virtual photon emitted by an electron

In a Feynman diagram, it is a single hit which creates the field of an electron. The spectrum is wrong, if we believe our own model. The Feynman model plays down low frequencies. There is no buildup of low frequencies from many hits. The Feynman model exaggerates the impact of high frequencies. The high-frequency error is corrected with regularization in QED.

The Feynman model is approximately right for mid-frequencies.

Question. The Feynman model is wrong for low frequencies. Why that does not show up as significant (e.g., ~ 10%) errors in Feynman calculations?

The simplest Feynman diagram - for an unknown reason - models in the right way classical relativistic Coulomb scattering. It might be that the same coincidence is the answer to the Question above.

The bare mass of the electron is 1.022 MeV?

Let us first have an electron without the interaction with the electromagnetic field. Its mass-energy might be 1.022 MeV. Once we couple it to the electromagnetic field, it sinks to a lower potential. It is a good guess that the electron sinks to a potential -1.022 MeV. The virial theorem suggests that the entire energy of the system, 511 keV, is then in the electric field of the electron.

If the electron moves in the zitterbewegung loop, the mass-energy of the electron looks reduced because the far field does not have time to react. The acceleration in the zitterbewegung loop is moderate. What about high-energy collisions?

Suppose that we hit the electron with another particle. If the collision energy is ~ 1 MeV or larger, the electron can climb up from its potential pit. Does that have consequences which we could observe? The electron will move slower than an electron with a mass of 511 keV. After the collision, the electron will quickly sink back into a potential pit and emit 511 keV in radiation. The electron would for a short time be in an excited state - excited in its own field.

When the electron sinks back, the radiation which it emits can be confused with bremsstrahlung.

Excitation in the own field is somewhat fuzzy a concept. We might say that the field around the electron is excited, instead of the electron itself.