Path integral approach to quantum gravity

Abstract

In this thesis, we study path integral quantization of gravity. The general features of the approach are first studied in quantum mechanics and quantum field theory. The advantages and disadvantages of the Lorentzian and Euclidean approaches are discussed in detail. In the context of semiclassical approximation of path integrals, the structure of a typical term in the expansion is studied for scalar, vector, and symmetric rank 2 tensor fields. Then we study the path integral approach to gravity and delve deep into the problems with Euclidean gravity. The subtleties associated with Hawking's prescription for the conformal factor problem are studied in detail. An alternative resolution of the problem in linearized gravity is reviewed. It is shown that proper gauge-fixing of the linearized gravity path integral cures the problem in linearized gravity. This is followed by a study of functional determinants which is essential for computing semiclassical expansion of path integrals.