Summary: The self-localized quasi-particle excitation of the electron-positron field (EPF) is found for the first time in the framework of a standard form of the quantum electrodynamics. This state is interpreted as the "physical" electron (positron) and it allows one to solve the following problems: i) to express the "primary" charge $e_{0}$ and the mass $m_{0}$ of the "bare" electron in terms of the observed values of $e$ and $m$ of the "physical" electron without any infinite parameters and by essentially nonperturbative way; ii) to consider $\mu $-meson as another self-localized EPF state and to estimate the ratio $m_{\mu }/m$; iii) to prove that the self-localized state is Lorentz-invariant and its energy spectrum corresponds to the relativistic free particle with the observed mass $m$; iv) to show that the expansion in a power of the observed charge $e <$< 1 corresponds to the strong coupling expansion in a power of the "primary" charge $e^{-1}_{0} ~ e$ when the interaction between the "physical" electron and the transverse electromagnetic field is considered by means of the perturbation theory and all terms of this series are free from the ultraviolet divergence.

81V05, 81V10, 83C47

renormalization, Dirac electron-positron vacuum, nonperturbative theory