Semiclassical approximation of the Wheeler–DeWitt equation: arbitrary orders and the question of unitarity

We extend the Born–Oppenheimer type of approximation scheme for the Wheeler–DeWitt equation of canonical quantum gravity to arbitrary orders in the inverse Planck mass squared. We discuss in detail the origin of unitarity violation in this scheme and show that unitarity can be restored by an appropriate modification which requires back reaction from matter onto the gravitational sector. In our analysis, we heavily rely on the gauge aspects of the standard Born–Oppenheimer scheme in molecular physics.