The "cutting-off method" proposed in Part I is equivalent to a field theory based on Maxwell's equations supplemented by Yukawa's equations, both fields having the same point charges as sources. The chief result is a finite self-energy $W=\frac{e^2}{2r_0}$ and a modified Coulomb potential $\left(\frac{e}{r}\right)[1-\exp (\frac{-r}{r_0}\left)\right]$, also derivable from a Hamiltonian in Fourier form. For accelerated motions the field theory yields a finite force of inertia ($-m\ddot{x}$) together with the universal damping term in first approximation. Small additional terms reflect the "structure" of the electron. Radiation and self-force of a vibrating electron are discussed, and the perturbation problem is formulated. The exact integration of Yukawa's field equation is given in Section 9. Our results are related to Born-Infeld's unitary field theory and Dirac's theory of the classical electron, in particular with respect to waves of velocity larger than $c$. The electronic mass $m$ is the result of photons of rest mass zero and mesons of rest mass $M=m·2·137=274m$.

• Received 9 July 1941

DOI:https://doi.org/10.1103/PhysRev.60.514