Diffeomorphism-invariant observables and their nonlocal algebra

By William Donnelly, S. Giddings. 2015

184 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/d18d47362e8f7d16e02aac2e0bd634f765593441

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In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Observables, gravitational dressing, and obstructions to locality and subsystems (2016, background): “This dressing makes these observables nonlocal, as was explicitly described in [2, 3].”
Symmetries in Quantum Field Theory and Quantum Gravity (2018, background): “The reader may consult [25, 128–133] for more details on the algebra of these kinds of operators.”
Bulk locality from modular flow (2017, background): “One normally thinks of this in terms of gravitational dressing: the bulk operator has its own gravitational field which gives a non-trivial commutator in the boundary, see [34] for more details.”
The Ryu–Takayanagi Formula from Quantum Error Correction (2016, background): “These operators will commute to all orders in perturbation theory with operators from which their entire geodesics are spacelike separated [1,63], so provided that their geodesics lie entirely in EA or EA then they will be in M or M ′ respectively, and they will commute with the area operator on the”