Unitary evolution, canonical variables and vacuum choice for general
  quadratic Hamiltonians in spatially homogeneous and isotropic space-times
  Quantization of arbitrary free scalar fields in spatially homogeneous and
isotropic space-times is considered. The quantum representation allowing a
unitary evolution for the fields is taken as a requirement for the theory.
Studying the group of linear canonical transformations, we show the relations
between unitary evolution and choice of canonical variables. From these
relations we obtain the conditions on the Hamiltonian such that there are
canonical variables for which the field has unitary evolution. We then compute
the linear transformation leading to these variables, also proving that they
are unique. We obtain these results by developing the asymptotic analysis of
the fields using the action angle variables, which proves to be a
generalization of the usual Wentzel-Kramers-Brillouin approximation. These
tools allow us to re-frame the adiabatic vacuum condition in a extensible
format by using the action angle variables to relate these vacuum choices to
those where the particle number density does not depend on angle (fast)
variables. Finally, we develop a larger set of canonical variables relating the
adiabatic vacuum conditions with the smearing of the quantum fields. This set
of canonical variables also connects the adiabatic vacuum conditions with the
instantaneous Hamiltonian diagonalization vacuum choice.
