Consistent Canonical Quantization of Gravity: Recovery of Classical GR from BRST-invariant Coherent States

We perform canonical quantization of General Relativity, as an effective quantum field theory below the Planck scale, within the BRST-invariant framework. We show that the promotion of constraints to dynamical equations of motion for auxiliary fields leads to the healthy Hamiltonian flow. In particular, we show that the classical properties of Einstein's gravity, such as vanishing Hamiltonian modulo boundary contribution, is realized merely as an expectation value in appropriate physical states. Most importantly, the physicality is shown not to entail trivial time-evolution for correlation functions. In the present approach we quantize the theory once and for all around the Minkowaski vacuum and treat other would-be classical backgrounds as BRST-invariant coherent states. This is especially important for cosmological spacetimes as it uncovers features that are not visible in ordinary semi-classical treatment. The Poincar\'e invariance of the vacuum, essential for our quantization, provides strong motivation for spontaneously-broken supersymmetry.