Electron as soliton: Nonlinear theory of dielectric polarization

Abstract

We describe a class of theories of dielectric polarization and a species of solitons in these theories. The solitons, made entirely out of the polarization field, have quantized values of the electric charge and can be interpreted as electrons and holes. A soliton-antisoliton pair is an exciton. We present numerical evidence that the elementary soliton is stable.