  We analyze the equations of quantum electrodynamics and establish that the
electron must be described by two bispinors that satisfy two mutually connected
Dirac equations. The equations of the electronic and electromagnetic fields are
reformulated in terms of c-numbers, which enables one to elucidate the
structure of the electron. Although the equations obtained allow only for
numerical solution, some characteristics of the electron, in particular its
size, can be found at this stage. It is shown also that the Dirac equation
should, instead of the mass of the electron, contain a combination involving
the electron Compton wavelength. In this case the equations obtained can be
used not only for the description of the electron but also for the description
of other leptons, which will allow one to find the mass spectrum of leptons.
