Euclidean Quantum Gravity in Light of Spectral Geometry

Abstract

A proper understanding of boundary-value problems is essential in the attempt of developing a quantum theory of gravity and of the birth of the universe. The present paper reviews these topics in light of recent developments in spectral geometry, i.e. heat-kernel asymptotics for the Laplacian in the presence of Dirichlet, or Robin, or mixed boundary conditions; completely gauge-invariant boundary conditions in Euclidean quantum gravity; local vs. non-local boundary-value problems in one-loop Euclidean quantum theory via path integrals.

31 pages, plain Tex. Submitted to the Proceedings of the Workshop: "Spectral Geometry of Manifolds with Boundary and Decomposition of Manifolds", Roskilde (Denmark), August 2003. Editors: Bernhelm Booss-Bavnbek, Gerd Grubb, Krzysztof P. Wojciechowski