Semiclassical approximations for gravity and the issue of backreaction

Semiclassical approximations, which are useful in the study of a quantum system interacting with a classical system, are studied and compared. A toy quantum mechanical model with two degrees of freedom (which mimics the features of gravity interacting with quantum fields) is used for illustration. In particular, the author considers the Born-Oppenheimer approximation (BOA) (corresponding to G to 0 at fixed h(cross)), the effective action approach (h(cross) to 0 at fixed G) and their combinations. He shows that in the strict BOA limit there is no backreaction on gravity. Gravity is described by classical equations and the fields are quantised in that background. In the effective action approach one can obtain a semiclassical description for gravity, if certain stringent requirements are satisfied. In most situations of interest these conditions will not be met and the O(h(cross)) contribution from gravitons will be comparable to that from quantum fields. He studies the system using both the Schrodinger equation and path integrals and indicates the correspondence