Nonlocal Ghost Formalism for Quantum Gravity

Nonlocal boundary conditions for Euclidean quantum gravity have been proposed in the recent literature. Such boundary conditions are here required to be partially invariant under a class of nonlocal transformations on metric perturbations. The corresponding ghost operator is a pseudo-differential operator, subject to nonlocal boundary conditions whose form is fixed, implicitly, by the request of invariance of part of the boundary conditions on metric perturbations. One thus gets a complete scheme, although technically involved, for a nonlocal formulation of Euclidean quantum gravity