Soliton-like solution in quantum electrodynamics

TL;DR

This paper introduces a new soliton-like solution in quantum electrodynamics using a self-consistent field approach, revealing collective excitations of the electron-positron field with relativistic energy properties.

Contribution

It presents the first derivation of a soliton-like solution in QED through a self-consistent method, incorporating a canonical transformation for relativistic analysis.

Findings

Discovery of a soliton-like solution in QED

Derivation of the relativistic energy dispersion relation for the soliton

Application of a self-consistent field method inspired by superconductivity

Abstract

A novel soliton-like solution in quantum electrodynamics is obtained via a self-consistent field method. By writing the Hamiltonian of quantum electrodynamics in the Coulomb gauge, we separate out a classical component in the density operator of the electron-positron field. Then, by modeling the state vector in analogy with the theory of superconductivity, we minimize the functional for the energy of the system. This results in the equations of the self-consistent field, where the solutions are associated with the collective excitation of the electron-positron field---the soliton-like solution. In addition, the canonical transformation of the variables allowed us to separate out the total momentum of the system and, consequently, to find the relativistic energy dispersion relation for the moving soliton.