  The decoherent histories approach to quantum theory is applied to a class of
reparametrization invariant models, which includes systems described by the
Klein-Gordon equation, and by a minisuperspace Wheeler-DeWitt equation. A key
step in this approach is the construction of class operators characterizing the
questions of physical interest, such as the probability of the system entering
a given region of configuration space without regard to time. In
non-relativistic quantum mechanics these class operators are given by
time-ordered products of projection operators. But in reparametrization
invariant models, where there is no time, the construction of the class
operators is more complicated, the main difficulty being to find operators
which commute with the Hamiltonian constraint (and so respect the invariance of
the theory). Here, inspired by classical considerations, we put forward a
proposal for the construction of such class operators for a class of
reparametrization-invariant systems. They consist of continuous infinite
temporal products of Heisenberg picture projection operators. We investigate
the consequences of this proposal in a number of simple models and also compare
with the evolving constants method.
