S.Manaenkov (PNPI)

Can classical point-like electron have finite electromagnetic and total masses?

It is argued that the gravitational force can play a crucial role in the structure of leptons. The exact Reissner-Nordstr$\ddot{\rm{\bf{o}}}$m solution of the Maxwell and Einstein equations corresponding the gravitational field configuration localized in the region with the range of about $10^{-34}$ cm is discussed. It is shown that the electromagnetic mass of the classical electron is finite and by about $10^{21}$ times larger than the experimental electron mass. The contribution of the gravitational interaction to the total electron mass is negative and makes the mass equal to its experimental value It is discussed a scenario when leptons and quarks did not exist as fundamental fields of the matter and could be localized soliton-like solutions of equations for the fundamental fields responsible for the electromagnetic, strong, weak, and gravitational interactions.