Diffeomorphism-invariant observables and their nonlocal algebra

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.

Quantum-gravity effects outside the horizon spark black to white hole tunneling

“…These are suppressed in the approximation provided by local quantum field theory on a curved geometry. Their possibility, however, cannot be ruled out in a non-perturbative quantum theory of gravity, and is increasingly considered plausible by a number of authors, on the basis of diverse considerations [26][27][28][29]. These converge in suggesting that local quantum field theory might fail to account for quantum gravity phenomena.…”

Quantum state reduction: Generalized bipartitions from algebras of observables

“…The procedure for constructing the BPT is essentially what we did in the proof of Lemma 4.9 16 It should be noted that the selection of BPOs is not unique and depends on the arbitrary selection of paths between the elements of the MSMP. This freedom, however, only changes the individual BPOs by a constant factor, which does not affect the generalized bipartition structure captured by the BPT.…”

“…In order to construct the aforementioned BPT, we will first select a subset of path isometries in the network to be the BPOs. 16 Let Π v q k be all the elements of the MSMP that belong to the connected component q and let Π v q 1 be a single, arbitrarily chosen, element. We first select the path isometries S q k1 by arbitrarily choosing a path from Π v q 1 to each Π v q k for k > 1 and S q 11 := Π v q 1 .…”

“…Then we would like to be able to sensibly construct a reduced state even when the theory has an obstructing symmetry, such as the state of a gauge theory or conformal field theory on an interval, or the state of a spatial subregion in a diffeomorphism-invariant theory like general relativity. Such a construction is provided by the edge modes program [14][15][16][17] (see also [66]). On the quantum-mechanical level one looks for an embedding of the physical Hilbert space, which need not factorize, into a larger Hilbert space with some desired factorization properties, such as the existence of spatial intervals.…”

“…When the theory has a gauge symmetry, however, the physical Hilbert space is restricted to states which obey global constraints like a Gauss law, and we cannot consistently restrict to subregions in a gauge-invariant way. The approach of the edge modes program [14][15][16][17] is to embed the physical Hilbert space into a larger, "ungauged" Hilbert space in which the constraints have been removed and subregions are well-defined.…”