There are different points of view about how quantum cosmology should be
constructed, and also about the interpretation of the formalism. A reason
for this is a peculiar problem which comes from the fact that we are looking
for a theory of the whole universe: while one usually deals with systems
for which the meaning of "evolution" is clear as it is possible to assume
that there is something external which plays the role of a clock, this is not
possible in cosmology. There are then two possibilities: one could abandon
the idea of a description with a clear notion of time; or we can assume that
a subset of the variables describing the state of the universe can be used as a
clock for the remaining of the system. Here the reader will find a proposal
within this last framework; this proposal is restricted to minisuperspace,
models, and consists in identifying a time among the canonical variables
by means of gauge fixation and then to obtain the transition amplitude in
the form of a path integral with a clear separation between time and true
degrees of freedom