The path-integral approach to quantum gravity

Three main approaches to quantizing gravity are summarized: the operator approach, the canonical approach and the path-integral approach. It is shown how the path integral approach can be applied to the quantization of gravity and how it leads to the concepts of black hole temperature and intrinsic quantum mechanical entropy. The discussion is under the following heads: the action in general relativity; complex spacetime; the indefiniteness of the gravitational action; the stationary-phase approximation; zeta function regularization; the background fields (some positive-definite metrics which are solutions of the Einstein equations in vacuum or with a Λ-term); gravitational thermodynamics; beyond one loop; spacetime foam. (U.K.)