In theoretical physics, it became clear in the frst part of the 20th century that

the self-energy of an electron's Coulomb field is infinite

and

part of the electron's mass has a non-electromagnetic origin.

First G. Mie in 1912 made an attempt to construct the electron as a field object. Then in the other direction H. Weil began work in 1918. Today Weil's way has an extensive development in quantum field theory.

Mie's way today is neglected, because it is impossible from the parameters of the electromagnetic field to construct the electromagnetic jet These parameters are: the potential four vector A(x) and fields be vector

(Clifford algebra formalism is always used.)

When in electrons mass give contribution another field then where it is? In Mie's time the gravitation field and electromagnetic field were known and it was clear that the gravitation field did not contribute any essential part of the electron's mass. Today the existence of the weak interaction and strong interaction are known. The electron is not affected by the strong interaction. Then weak or more trifling compose to it interaction is connect with electromagnetic field. From other reasons today in quantum field theory electromagnetic and weak interactions are joint in electroweak interaction But electron's parameters bring in this model by hand.

By unknown reason it is remain beyond attention of physicists that exist the classical field which connect between themselves all type of forces. Regard what it is. In general case any physical field have non zero mass density. Then in classical physics is parameter u(x) which is local four velocity vector a field. If this four vector itself is potential of some field (call it w-field) then from Bohr's coherence principle , which is one of the general physical principles , forces of this field are following

In case u² = 1 quantity is usual mechanical acceleration. In the typical case

(as examples: for scalar photons = Coulomb field u² > 0, for longitudinal photons=magnetic field u² < 0) and w-field by their physical sense is the bearer of inertial (typically virtual) forces.

If one takes into account the w-field then it is easy to construct electromagnetic jet, lagrangian for self interacting electromagnetic field, Maxwell's nonlinear equations, the nonlinear Coulomb field, extended Yukava potential, etc.

Simultaneous symmetry between electromagnetic and weak interactions and data about Lamb shift give the possibility to regard the four velocity vector as the classical potential of the weak interaction.