Nonuniform external fields and vacuum properties in a two-dimensional gauge theory

Abstract
We compute the effective action for scalar electrodynamics in two-dimensional space-time, to the one-loop order, for a two-parameter solitonlike family of nonuniform electric fields. We find that the vacuum is always dia-electric for this class of fields. The electric permeability results to be a decreasing function of the field strength and an increasing function of the field extension.