Magnetic permeability of constrained scalar QED vacuum

We compute the influence of boundary conditions on the effective Lagrangian of scaler QED for the case of a pure magnetic field. The boundary conditio ns assumed here constrain the quantum scaler field but not the radiation fi eld, so that the effect to be considered already appears at the one-loop le vel. The boundary conditions generate new contributions to the effective La grangian much in the same way as a material pressed between two plates exhi bits new magnetic properties. For the case of a periodic boundary condition we show that the bosonic vacuum behaves as if it were a diamagnetic medium . Our results show that the vacuum permeability has a linear term that is c ompletely absent when there is no boundary condition. (C) 2000 Elsevier B.V . All rights reserved.