Global structure of euclidean quantum gravity

Abstract

Euclidean quantum gravity (EQG) separates into a local theory and a global theory. The local theory operates in every compact $d$-manifold with boundary to produce a state on the boundary. The global theory then sums these boundary states over the diffeomorphism classes of $d$-manifolds with boundary to make the Hartle-Hawking state. Global EQG is formulated here as classical statistical physics. The Hartle-Hawking state is the probability measure of a mathematically natural classical statistical system, analogous to the functional measure of euclidean quantum field theory. General principles of global EQG determine the numerical weights $w(M)$ in the sum over diffeomorphism classes $M$.