Finite field-energy of a point charge in QED

We consider a simple nonlinear (quartic in the fields) gauge-invariant modification of classical electrodynamics, which possesses a regularizing ability sufficient to make the field energy of a point charge finite. The model is exactly solved in the class of static central-symmetric electric fields. Collation with quantum electrodynamics (QED) results in the total field energy about twice the electron mass. The proof of the finiteness of the field energy is extended to include any polynomial selfinteraction, thereby the one that stems from the truncated expansion of the Euler-Heisenberg local Lagrangian in QED in powers of the field strenth.