  We study the effect of boundary conditions on vacuum polarization for charged
scalar fields in two space-time dimensions. We find that both Dirichlet and
Neumann boundary conditions lead to screening. In the Dirichlet case, the
vacuum polarization charge density vanishes at the boundary, whereas it attains
its maximum there for Neumann boundary conditions. At a critical field
strength, the vacuum polarization diverges for Neumann boundary conditions, an
effect due to the instability of the lowest energy mode in the presence of the
external field.
