  This paper continues the investigation of the Casimir effect with the use of
the algebraic formulation of quantum field theory in the initial value setting.
Basing on earlier papers by one of us (AH) we approximate the Dirichlet and
Neumann boundary conditions by simple interaction models whose nonlocality in
physical space is under strict control, but which at the same time are
admissible from the point of view of algebraic restrictions imposed on models
in the context of Casimir backreaction. The geometrical setting is that of the
original parallel plates. By scaling our models and taking appropriate limit we
approach the sharp boundary conditions in the limit. The global force is
analyzed in that limit. One finds in Neumann case that although the sharp
boundary interaction is recovered in the norm resolvent sense for each model
considered, the total force per area depends substantially on its choice and
diverges in the sharp boundary conditions limit. On the other hand the local
energy density outside the interaction region, which in the limit includes any
compact set outside the strict position of the plates, has a universal limit
corresponding to sharp conditions. This is what one should expect in general,
and the lack of this discrepancy in Dirichlet case is rather accidental. Our
discussion pins down its precise origin: the difference in the order in which
scaling limit and integration over the whole space is carried out.
