Space-time dynamics of the vacuum's polarization charge density

Using numerical solutions to the quantum-field theoretical Dirac equation, we study the space-time evolution of the vacuum's polarization charge and current densities induced by an external electric force in one spatial dimension. We discuss a simple analytical model that can predict the dynamics of the polarization dynamics for arbitrary external force configurations. We then study the corrections to these predictions when the external force becomes supercritical and real electron-positron pairs can be created. By coupling the Dirac equation to the Maxwell equations, we examine how the dynamics of the polarization density is affected, if we allow the corresponding induced charges to interact with each other.