  We address the issue of inequivalent Fock representations in Quantum Field
Theory in a curved homogenous and anisotropic background, namely
Kantowski-Sachs spacetime. A family of unitarily equivalent Fock
representations that are invariant under the spatial isometries and implement a
unitary dynamics can be achieved by means of a field redefinition that consists
of a specific anisotropic scaling of the field configuration and a linear
transformation of its momentum. Remarkably, we show that this kind of field
redefinition is in fact unique under our symmetry and unitary requirements.
However, the physical properties of the Hamiltonian dynamics that one obtains
in this way are not satisfactory, inasmuch as the action of the Hamiltonian on
the corresponding particle states is ill defined. To construct a quantum theory
without this problem, we need a further canonical transformation that is time-
and mode-dependent and is not interpretable as an anisotropic scaling. The old
and new Fock representations, nevertheless, are unitarily equivalent. The
freedom that is introduced when allowing for this further canonical
transformation can be fixed by demanding an asymptotic diagonalization of the
Hamiltonian and a minimal absorption of dynamical phases. In this way, the
choice of vacuum and the associated Fock representation are asymptotically
determined.
