  Linear free field theories are one of the few Quantum Field Theories that are
exactly soluble. There are, however, (at least) two very different languages to
describe them, Fock space methods and the Schroedinger functional description.
In this paper, the precise sense in which the two representations are related
is reviewed. Several properties of these representations are studied, among
them the well known fact that the Schroedinger counterpart of the usual Fock
representation is described by a Gaussian measure. A real scalar field theory
is considered, both on Minkowski spacetime for arbitrary, non-inertial
embeddings of the Cauchy surface, and for arbitrary (globally hyperbolic)
curved spacetimes. As a concrete example, the Schroedinger representation on
stationary and homogeneous cosmological spacetimes is constructed.
