  The motion of a system of particles under electromagnetic interaction is
considered. Under the assumption that the force acting on an electric charge is
given by the sum of the electromagnetic fields produced by any other charged
particles in its neighborhood, we prove that the vector potential of the
electromagnetic field has to be considered for the balance of kinetic momentum.
The theory cannot be quantized in the usual form -- because it involves a mass
matrix that depends on spatial variables -- and the Hamilton's function becomes
singular at a distance equal to the geometric mean of the electrodynamic
radiuses of electrons and protons.
