Towards a Background Independent Formulation of Perturbative Quantum Gravity

The recent formulation of locally covariant quantum field theory may open the way towards a background independent perturbative formulation of Quantum Gravity. 1 Problems of perturbative Quantum Gravity In quantum field theory the fields are defined as operator-valued distributions on a given spacetime, and many of their properties, in particular the commutativity at spacetime separated points, depend in a crucial way on properties of the background. In a perturbative approach to quantum gravity, one decomposes the metric gμν into a background metric ημν and a quantum field hμν , which is treated according to standard methods in perturbation theory. The (up to now observed) effects of this quantum field are very small, hence a perturbative approach seems to be appropriate. There are, however, several obstructions which raise doubts on the validity of the perturbative approach: