Elementary Particles’ Electrodynamics

We suggest a field theory based on a generalization of Maxwell’s equations of electromagnetism, which allows one to describe the various elementary particles’ structures. It seems to us, that such a theory must exist because under suitable reactions, particles can turn into particles of other forms and that the photon which partakes in many reactions, being a quantum of electromagnetic field, is described by the Maxwell equations. The fact that particles are supposed to have an internal structure and not be singular points, as is generally accepted in modern physics, supports Plank’s hypothesis that every free particle is associated with a harmonic oscillation related to its internal energy. The photon can serve as an example, whose internal motion is described by the interaction of electric and magnetic fields. In order for a particle to exist on its own, that is without external influence, the equations that describe its field, in our opinion, must be compatible with each other (source being determined by the field, and the field by the source) and nonlinear. Let us note that the photon is an exception to this rule, since it is defined by linear equations. This is related, apparently, to the fact that it travels with the maximum speed—the speed of light c. Unlike in Maxwell’s theory where sources are independent of the field that they generate, we propose a model with nonlinear self-compatible equations in which the sources happen to be quadratic functions of the electric and magnetic fields. We give an approximate solution to the nonlinear equation for the electron and we show that the structure of its electric field is asymptotically determined by Coulomb’s law away from the particle’s center, while near the center the field changes its nature.