  We address the issue of the infinite ambiguity that affects the construction
of a Fock quantization of a Dirac field propagating in a cosmological spacetime
with flat compact sections. In particular, we discuss a physical criterion that
restricts to a unique possibility (up to unitary equivalence) the infinite set
of available vacua. We prove that this desired uniqueness is guaranteed, for
any possible choice of spin structure on the spatial sections, if we impose two
conditions. The first one is that the symmetries of the classical system must
be implemented quantum mechanically, so that the vacuum is invariant under the
symmetry transformations. The second and more important condition is that the
constructed theory must have a quantum dynamics that is implementable as a
(non-trivial) unitary operator in Fock space. Actually, this unitarity of the
quantum dynamics leads us to identify as explicitly time dependent some very
specific contributions of the Dirac field. In doing that, we essentially
characterize the part of the dynamics governed by the Dirac equation that is
unitarily implementable. The uniqueness of the Fock vacuum is attained then
once a physically motivated convention for the concepts of particles and
antiparticles is fixed.
