Perturbative Gravity Expansions

I have been asked to describe the status of perturbative expansions of gravity theories. This is a fairly active and interesting subject. I will try to be brief, because I have a lot to say about string theory, which is the main subject of my lectures at this school. The motivation for studying perturbative gravity expansions is to ascertain whether standard methods of quantum field theory are applicable to theories based on actions that contain the Einstein–Hilbert action. It was realized long ago that classical Einstein gravity in four dimensions, reinterpreted as a quantum theory, is probably nonrenormalizable. At the time, this was not considered an important problem, because relativists were not interested in quantum mechanics and particle physicists were not interested in gravity. That has changed dramatically over the past 30 years.