Some applications of the Riesz potential to the theory of the electromagnetic field and the meson field

Abstract

This paper contains some applications of the method of Marcel Riesz in the solution of normal hyperbolic differential equations, in particular the wave equation, where the known difficulties, due to the occurrence of divergent integrals, are avoided by a process of analytical continuation. In the theory of the electromagnetic field the method yields simple deductions of classical results, but also the results recently obtained by Dirac regarding the proper energy and proper momentum of an electron are obtained without any addition of new assumptions. The corresponding problem in Bhabha’s analogous theory for the neutral meson field are also studied.