  We compute the combined effect of confinement, an external magnetic field and
temperature on the vacuum of the charged scalar field using Schwinger's formula
for the effective action in the imaginary time formalism. The final result
reproduces an effective Lagrangian similar to the Heisenberg-Euler one in the
limit of no confinement, in the case of confinement it provides the necessary
corrections to this Lagrangian at each order of magnitude of the magnetic
field. The results show a finite temperature contribution to the vacum
permeability constant apart from the one due to confinement alone.

High Energy Physics - Theory