**Lorentz and gauge invariant self-localized excitation in the large-alpha QED**

**Abstract:**

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 *a* is supposed to be of a large value
(*a* >>1).

It is shown that in this case the entangled electron-positron excitation with non-zero integral charge can be
produced together with the electromagnetic field. Self-consistent equations for the localized charge distribution coupled
with the electromagnetic field are derived.

Soliton-like solution with a nonzero charge for these equations is calculated numerically. The gauge invariance of
this solution leads to the condition of the charge quantization. It is also proved that the dispersion law of the
soliton-like excitation is consistent with Lorentz invariance of the QED equations.

Joint work with *S.I. Feranchuk*.