  The Casimir force between two perfectly reflecting parallel plates is
considered. In a recent paper we presented generalised physical boundary
conditions describing perfectly reflecting parallel plates. These boundary
conditions are applicable to a field possessing any spin, and include the
well-known spin-1/2 and spin-1 boundary conditions as special cases. Here we
use these general boundary conditions to show that the allowed values of
energy-momentum turn out to be the same for any massless fermionic field and
the same for any massless bosonic field. As a result one expects to obtain only
two possible Casimir forces, one associated with fermions and the other with
bosons. We explicitly verify that this is the case for the fields up to spin-2.
A significant implication of our work is that periodic boundary conditions
cannot be applied to a fermionic field confined between two parallel plates.
