Finite Self-Energies in Radiation Theory. Part II

Abstract

The “cutting-off method” proposed in Part I is equivalent to a field theory basedon Maxwell’s equations supplemented by Yukawa’s equations, both fields having the samepoint charges as sources. The chief result is a finite self-energy W=e 2/2r o and a modified Coulomb potential (e/r)[1-exp (-r/r o)], also derivable from a Hamiltonian in Fourier form. For accelerated motions the field theory yields a finite force of inertia (—mx) 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.