Effect of boundaries on vacuum polarization and charge-pair production by a constant electric field

The effect of a strong constant electric field on the vacuum when boundary effects are taken into account (the Casimir effect) is studied. In the case of ''transverse confinement'' (confinement of particles in the plane perpendicular to the direction of the electric field) a closed analytic expression is obtained in the one-loop approximation for the real and imaginary parts of the effective Lagrangian in the entire range of variation of the field strength. In the case of ''longitudinal confinement'' the dielectric permittivity of the vacuum in a finite region and the intensity of charge-pair production are calculated and found to be considerably different from the standard formulas valid for an infinite medium