Soliton-like excitation in large-alpha QED

TL;DR

This paper investigates nonperturbative, soliton-like electron-positron excitations in large-alpha QED, deriving self-consistent localized solutions that exhibit charge quantization and Lorentz-invariant dispersion.

Contribution

It introduces a novel nonperturbative approach to find soliton-like excitations in large-alpha QED, including numerical solutions and charge quantization conditions.

Findings

Soliton solutions are numerically computed and shown to be unique for fixed coupling.

Charge quantization emerges naturally from non-overlapping n-soliton states.

Dispersion law aligns with Lorentz invariance of 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 $\alpha_0$ 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.