  We study a proposal for gauge-invariant correlation functions in perturbative
quantum gravity, which are obtained by fixing the geodesic distance between
points in the fluctuating geometry. These correlation functions are non-local
and strongly divergent, and we show how to renormalise them by performing a
"wave function renormalisation" of the geodesic embedding coordinates. The
result is finite and gauge-independent, but displays unusual features such as
double logarithms at one-loop order.

High Energy Physics - Theory;General Relativity and Quantum Cosmology