  Using functional integral methods, we study the Casimir effect for the case
of two infinite parallel plates in the QED vacuum, with (different) perfect
electromagnetic boundary conditions applied to both plates. To enforce these
boundary conditions, we add two Lagrange multiplier fields to the action. We
subsequently recover the known Casimir energy in two ways: once directly from
the path integral, and once as the vacuum expectation value of the 00-component
of the energy-momentum tensor. Comparing both methods, we show that the
energy-momentum tensor must be modified, and that it picks up boundary
contributions as a consequence. We also discuss electromagnetic
duality-invariance of the theory and its interplay with the boundaries by
generalizing the Deser-Teitelboim implementation of the duality transformation.
