Abstract
In these lectures I am going to describe an approach to Quantum Gravity using path integrals in the Euclidean regime i.e. over positive definite metrics. (Strictly speaking, Riemannian would be more appropriate but it has the wrong connotations). The motivation for this is the belief that the topological properties of the gravitational fields play an essential role in Quantum Theory. Attempts to quantize gravity ignoring the topological possibilities and simply drawing Feynman diagrams corresponding to perturbations around flat space have not been very successful: there seem to be an infinite sequence of undetermined renormalization parameters. The situation is slightly better with supergravity theories; the undetermined renormalization parameters seem to come in only at the third and higher loops around flat space but perturbations around metrics that are topologically non-trivial introduce undetermined parameters even at the one loop level [1] [27] as I shall show later on.
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Hawking, S.W. (1979). Euclidean Quantum Gravity. In: Lévy, M., Deser, S. (eds) Recent Developments in Gravitation. NATO Advanced Study Institutes Series, vol 44. Springer, Boston, MA. https://doi.org/10.1007/978-1-4613-2955-8_4
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