  In this paper the nonperturbative analysis of the spectrum for one-particle
excitations of the electron-positron field (EPF) is considered in the paper. A
standard form of the quantum electrodynamics (QED) is used but the charge of
the "bare" electron $e_0$ is supposed to be of a large value. It is shown that
in this case the quasi-particle can be formed with a non-zero averaged value of
the scalar component of the electromagnetic field (EMF). Self-consistent
equations for the distribution of charge density in the "physical" electron
(positron) are derived. A variational solution of these equations is obtained
and it defines the finite renormalization of the charge and mass of the
electron (positron). It is found that the coupling constant between EPF and EMF
and mass of the "bare" electron can be connected with the observed values of
the fine structure constant and the mass of the "physical" electron. It is also
shown that although the non-renormalized QED corresponds to the strong coupling
between EPF and EMF, the interaction between "physical" electron (positron)
with EMF is defined by the observed value of the coupling constant. It is
proved that the translational motion of the "physical" particle is separated
from its internal degrees of freedom. As a result the dependence of the
one-particle excitation energy on its total momentum corresponds to the
relativistic spectrum of a free particle with the observed value of mass.
Regularization of the terms of a series of the perturbation theory is due to
the form-factor of the "physical" electron (positron).
