Model for inner structure and mass spectrum of charged leptons

Abstract

We present a model where the lepton masses are the eigenvalues of relativistic nonlinear field equations. The eigenfunctions correspond in the model to lepton states with inner structure. In this picture the self-interaction leads to the bound state of electron described by the ground state solution. The variational approach based on minimization of the mass or the energy of the ground state solution is developed. The analytical solution yields the relation between the coupling constant $G_l$ of the self-interaction and the electron mass as $m_e\simeq 2.3\sqrt{\hbar c/G_l}$. This solution also leads to a finite `radius' of the electron which is about $1.9\lambda_e$ where $\lambda_e$ is the Compton length of electron.