Semiclassical approximation of the Wheeler-DeWitt equation: arbitrary orders and the question of unitarity. (arXiv:1802.01422v2 [gr-qc] UPDATED)
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.