Magnetic properties of confined bosonic vacuum

The effect of confinement on the bosonic vacuum under the action of an applied magnetic field is computed using Schwinger's formalism for the effective action. The final result reproduces an effective La-grangian similar to the Heisenberg-Euler one in the limit of no confinement and in the case of confinement provides the necessary corrections to this Lagrangian at each order of magnitude of the magnetic field. It also shows a new contribution changing the vacum permeability constant.