  A discussion of relativistic quantum-geometric mechanics on phase space and
its generalisation to the propagation of free, massive, quantum-geometric
scalar fields on curved spacetimes is given. It is shown that in an arbitrary
coordinate system and frame of reference in a flat spacetime, the resulting
propagator is necessarily the same as derived in the standard Minkowski
coordinates up to a Lorentz boost acting on the momentum content of the field,
which is therefore seen to play the role of Bogolubov transformations in this
formalism. These results are explicitly demonstrated in the context of a Milne
universe.
