On classical gravitational corrections to the functional Schrödinger equation

Abstract A full theory of quantum gravity is not yet available, and an approximation in which spacetime remains classical while matter is described by quantum fields is often physically and computationally appropriate. It is therefore of interest to investigate hybrid systems which describe the interaction of classical gravity with quantum matter. Such systems may provide valuable clues relevant to the search of a quantum theory of gravity. Furthermore, one should also consider the possibility that the gravitational field may not be quantum in nature; in that case, it would become necessary to search for a consistent hybrid description. It is known that the Wheeler-De Witt equation with coupling to quantum fields results in quantum gravitational corrections to the functional Schrödinger equation. A similar result can be obtained for some hybrid models where a classical gravitational field interacts with quantum matter fields. I use the approach of ensembles on configuration space to look at a hybrid model where matter is in the form of a quantized scalar field and determine the corresponding classical gravitational corrections to the functional Schrödinger equation.