Diffeomorphism-invariant observables and their nonlocal algebra

TL;DR

This paper constructs gauge-invariant, nonlocal observables in quantum gravity, extending Dirac's methods, and analyzes their algebra, revealing nonlocality especially in strong gravitational fields.

Contribution

It provides explicit constructions of gravitational observables analogous to QED operators, including those for moving particles, and studies their nonlocal algebra in quantum gravity.

Findings

Observables include Wilson-line and Coulombic operators.

Commutators of observables are nonlocal, especially in strong fields.

Nonlocality becomes significant in regions of strong gravity.

Abstract

Gauge-invariant observables for quantum gravity are described, with explicit constructions given primarily to leading order in Newton's constant, analogous to and extending constructions first given by Dirac in quantum electrodynamics. These can be thought of as operators that create a particle, together with its inseparable gravitational field, and reduce to usual field operators of quantum field theory in the weak-gravity limit; they include both Wilson-line operators, and those creating a Coulombic field configuration. We also describe operators creating the field of a particle in motion; as in the electromagnetic case, these are expected to help address infrared problems. An important characteristic of the quantum theory of gravity is the algebra of its observables. We show that the commutators of the simple observables of this paper are nonlocal, with nonlocality becoming significant in strong field regions, as predicted previously on general grounds.