  There is a formal analogy between the evolution of the universe, when this is
seen as a trajectory in the minisuperspace, and the worldline followed by a
test particle in a curved spacetime. The analogy can be extended to the quantum
realm, where the trajectories are transformed into wave functions that give us
the probabilities of finding the universe or the particle in a given point of
their respective spaces: the spacetime in the case of the particle and the
minisuperspace in the case of the universe. The wave function of the spacetime
and the matter fields, all together, can then be seen as a super-field that
propagates in the minisuperspace and the so-called third quantisation procedure
can be applied in a parallel way as the second quantisation procedure is
performed with a matter field that propagates in the spacetime. The super-field
can thus be interpreted as made up of universes propagating, i.e. evolving, in
the minisuperspace. The corresponding Fock space for the quantum state of the
multiverse is then presented. The analogy can also be used in the opposite
direction. The way in which the semiclassical state of the universe is obtained
in quantum cosmology from the quantum state of the universe allows us to
obtain, from the quantum state of a field that propagates in the spacetime, the
geodesics of the underlying spacetime as well as their quantum uncertainties or
dispersions. This might settle a new starting point for a different
quantisation of the spacetime coordinates.
