We study the solutions of the Fröhlich Hamiltonian eigenvalue problem that depend specifically on the properties of systems with infinite number of degrees of freedom. Our major concern is then to sort out those solutions which can be given on a separable Hilbert space and those that cannot, as apparently both types exist. The former solutions are then the only ones applicable to solid state problems, whereas the latter are not. An example of the latter is the usual translational invariant Fock approximation and of the former the translationally noninvariant Fock approximation. Although our major vehicle for studying these problems is the Fock approximation itself, most of our results can readily be extended beyond it. We also bring out some properties of the system which are due to the nonapplicability of the quasiparticle concept when one studies low lying excited states of the large polaron using certain dynamical approximations.