The Born - Oppenheimer approach to the matter - gravity system and unitarity

The Born - Oppenheimer approach to the matter - gravity system is illustrated in a simple minisuperspace model and the corrections to quantum field theory on a semiclassical background exhibited. Within such a context the unitary evolution for matter, in the absence of such phenomena as tunnelling or other instabilities, is verified and compared with the results of other approaches. Finally, simplifications associated with the use of adiabatic invariants to obtain the solution of the explicitly time-dependent evolution equation for matter are given.