  The problem of defining and constructing representations of the Canonical
Commutation Relations can be systematically approached via the technique of
{\it algebraic quantization}. In particular, when the phase space of the system
is linear and finite dimensional, the `vertical polarization' provides an
unambiguous quantization. For infinite dimensional field theory systems, where
the Stone-von Neumann theorem fails to be valid, even the simplest
representation, the Schroedinger functional picture has some non-trivial
subtleties. In this letter we consider the quantization of a real free scalar
field --where the Fock quantization is well understood-- on an arbitrary
background and show that the representation coming from the most natural
application of the algebraic quantization approach is not, in general, unitary
equivalent to the corresponding Schroedinger-Fock quantization. We comment on
the possible implications of this result for field quantization.
