Finite Self-Energies in Radiation Theory. Part III

The invariant field theory of Part II is interpreted, in agreement with F. Bopp, as Maxwell's theory with a linear differential relation between the fields $E$, $B$ and $D$, $H$ involving a new constant $k$ which measures the reciprocal radius of the electron. The former "mesonic field" of minimum frequency ${\nu }_0=\frac{\mathrm{kc}}{2\pi }$ represents polarization of the vacuum. The electron is a singularity in the $D$, $H$ field whereas $E$, $B$ remain finite. Instead of obeying dynamical equations of motion, the electron moves under the condition that the Lorentz force vanishes identically on the singularity, so that no work is done on the particle. All energy is located in the field. In this respect the theory is unitary. Electromagnetic and inert mass are identical. In contrast to Dirac's classical electron which is subject to advanced and retarded potentials and displays self-acceleration, the field theory works with retarded potentials only, and self-acceleration is avoided. Stable equilibrium between electrons and radiation is granted by spontaneous and induced transitions, similar to Einstein's derivation of Planck's radiation formula. In spite of displaying a magnetic moment the electron does not have magnetic self-energy, so that its radius is the ordinary electrostatic radius $\frac{1}{k}=\frac{{\epsilon }^2}{2m{c}^2}$. In contrast to Born-Infeld's non-linear theory, our field equations allow a Fourier representation as a basis for the quantum theory of Part IV.