Nonlinear corrections in basic problems of electro- and magneto-statics in the vacuum

We find third-power nonlinear corrections to the Coulomb and other static electric fields, as well as to the electric and magnetic dipole fields, as we work within QED with no background field. The nonlinear response function we base our consideration on is the fourth-rank polarization tensor, calculated within the local (infrared) approximation of the effective action. Therefore, the results are applicable to weakly varying fields. It is established that the nonlinear correction to magnetic moment of some baryons just matches, in the order of magnitude, the existing gap between its experimental and theoretical values.