1. Introduction

This is the second in a series of papers on the ``bulk'' properties of quantized fields. The first paper in the series [1] derived mechanical and thermodynamic properties of non-interacting quantized fields in finite volumes. The present paper discusses electrodynamic properties of quantized fields by considering the response of the ``vacuum'' state to external electric fields. The third paper in the series will discuss the response of quantized fields to external gravitational fields [2].

For simplicity, we consider primarily charged scalar fields in 1 + 1 spacetime dimensions. The fields are confined to a finite spatial interval, so that their modes are discrete, and may be found explicitly.

In Section 2, we give a formal description of the modes and vacuum state for a charged scalar field in an external electric field. Section 3 treats in some detail the simple case of a field satisfying Dirichlet boundary conditions. For weak external electric fields, the ground state of the field exhibits vacuum polarization and behaves like a polarizable macroscopic medium, partially screening the applied electric field. Section 3 also considers nonclassical phenomena and instabilities which appear for larger electric fields.

Section 4 treats fields with general boundary conditions. In some cases, ``vacuum polarization'' is found to ``antiscreen'' the applied electric field, rather than screening like a polarizable medium. This behaviour is connected with the appearance of instabilities.

Sections 3 and 4 use the ``external field approximation,'' which accounts for the effect of the external electric field on the modes of the field, but ignores the electromagnetic ``back reaction'' of the field on itself. Section 5 describes a self-consistent semiclassical procedure which includes the effects of the back reaction. This procedure yields accurate results for large external electric fields so long as the charge on the field is sufficiently small. Instabilities which appeared in the external field approximation are found to be absent when back reaction effects are included.

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