Nonlocal Ghost Formalism for Quantum Gravity

TL;DR

This paper introduces a nonlocal ghost formalism for quantum gravity, extending concepts from quantum particle theory with boundary conditions to gravitational fields, highlighting the role of pseudo-differential operators in maintaining gauge invariance.

Contribution

It develops a novel nonlocal ghost formalism for quantum gravity that ensures boundary condition invariance under diffeomorphisms using pseudo-differential operators.

Findings

Boundary conditions compatible with diffeomorphism invariance involve pseudo-differential operators.

The formalism extends nonlocal boundary conditions from quantum mechanics to gravity.

Gauge-field and ghost operators are shown to be pseudo-differential operators in this framework.

Abstract

The quantum theory of a free particle on a portion of two-dimensional Euclidean space bounded by a circle and subject to non-local boundary conditions gives rise to bulk and surface states. Starting from this well known property, a counterpart for gravity is here considered. In particular, if spatial components of metric perturbations are set to zero at the boundary, invariance of the full set of boundary conditions under infinitesimal diffeomorphisms is compatible with non-local boundary conditions on normal components of metric perturbations if and only if both the gauge-field operator and the ghost operator are pseudo-differential operators in one-loop quantum gravity.