  Hamiltonian constraints feature in the canonical formulation of general
relativity. Unlike typical constraints they cannot be associated with a
reduction procedure leading to a non-trivial reduced phase space and this means
the physical interpretation of their quantum analogues is ambiguous. In
particular, can we assume that `quantisation commutes with reduction' and treat
the promotion of these constraints to operators annihilating the wave function,
according to a Dirac type procedure, as leading to a Hilbert space equivalent
to that reached by quantisation of the problematic reduced space? If not, how
should we interpret Hamiltonian constraints quantum mechanically? And on what
basis do we assert that quantisation and reduction commute anyway? These
questions will be refined and explored in the context of modern approaches to
the quantisation of canonical general relativity.
