  The Casimir force between two conducting planes is considered in both the
electromagnetic and scalar field cases. This is done by the usual summation
over energy eigenmodes of the system as well as by a calculation of the stress
tensor in the region between the planes. The latter case requires that careful
attention be given to singular operator products, an issue which is
accommodated here by invoking the point separation method in conjunction with a
scalar cutoff. This is shown to yield cutoff dependent and divergent
contributions to the Casimir pressure which are dependent on the separation
parameters, but entirely consistent with Lorentz covariance. Averaging over the
point splitting parameters allows finite results to be obtained, but fails to
yield a unique Casimir force.
