Vacuum polarization near boundaries

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.

Automated summary

The study explores the impact of boundary conditions on vacuum polarization for charged scalar fields in two-dimensional space-time. It is found that both Dirichlet and Neumann boundary conditions result in screening effects. The vacuum polarization charge density vanishes at the boundary under Dirichlet conditions, while reaching its maximum under Neumann conditions. At a critical field strength, the vacuum polarization diverges for Neumann boundary conditions due to the instability of the lowest energy mode in the presence of an external field.