Soliton-like excitation in large-alpha QED

The nonperturbative analysis of the one-particle excitation of the electron-positron field is made in the paper. The standard form of quantum electrodynamics (QED) is used but the coupling constant $\alpha_0$ is supposed to be of a large value ($\alpha_0 \gg 1$). It is shown that in this case the quasi-particle excitation can be produced together with the non-zero scalar component of the electromagnetic field. Self-consistent equations for spatially localized charge distribution coupled with an electromagnetic field are derived. Soliton-like solution with a nonzero charge for these equations are calculated numerically. The solution proves to be unique if the coupling constant is fixed. It leads to the condition of charge quantization if the non-overlapping $n$-soliton states are considered. It is also proved that the dispersion law of the soliton-like excitation is consistent with Lorentz invariance of the QED equations.