  The microcanonical density matrix in closed cosmology has a natural
definition as a projector on the space of solutions of Wheeler-DeWitt
equations, which is motivated by the absence of global non-vanishing charges
and energy in spatially closed gravitational systems. Using the BRST/BFV
formalism in relativistic phase space of gauge and ghost variables we derive
the path integral representation for this projector and the relevant
statistical sum. This derivation circumvents the difficulties associated with
the open algebra of noncommutative quantum Dirac constraints and the
construction/regularization of the physical inner product in the subspace of
BRS singlets. This inner product is achieved via the Batalin-Marnelius gauge
fixing in the space of BRS-invariant states, which in its turn is shown to be a
result of truncation of the BRST/BFV formalism to the "matter" sector of
relativistic phase space.
