  The Casimir effect is a physical manifestation of zero point energy of
quantum vacuum. In a relativistic quantum field theory, Poincar\'e symmetry of
the theory seems, at first sight, to imply that non-zero vacuum energy is
inconsistent with translational invariance of the vacuum. In the setting of two
uniform boundary plates at rest, quantum fields outside the plates have
(1+2)-dimensional Poincar\'e symmtry. Taking a massless scalar field as an
example, we have examined the consistency between the Poincar\'e symmetry and
the existence of the vacuum enegy. We note that, in quantum theory, symmetries
are represented projectively in general and show that the Casimir energy is
connected to central charges appearing in the algebra of generators in the
projective representations.
