Graviton corrections to the Newtonian potential using invariant observables

Abstract

We consider the effective theory of perturbative quantum gravity coupled to a point particle, quantizing fluctuations of both the gravitational field and the particle’s position around flat space. Using a recent relational approach to construct gauge-invariant observables, we compute one-loop graviton corrections to the invariant metric perturbation, whose time-time component gives the Newtonian gravitational potential. The resulting quantum correction consists of two parts: the first stems from graviton loops and agrees with the correction derived by other methods, while the second one is sourced by the quantum fluctuations of the particle’s position and energy-momentum, and may be viewed as an analog of a “Zitterbewegung”. As a check on the computation, we also recover classical corrections which agree with the perturbative expansion of the Schwarzschild metric.

A metric for Planck Stars derived from Gravity in Asymptotic Safety

“…On the other hand, corrections of quantum origin to the classical Newtonian potential have been elaborated by several researchers [30,31,32,33,34,35,36,37,38] in the last three decades or so. In particular, it was pointed out by Donoghue [31,34] that the standard perturbative quantization of Einstein gravity leads to a well defined, finite prediction for the leading large distance quantum correction to Newtonian potential.…”

“…On the other hand, by reformulating General Relativity as an effective quantum field theory of gravity at low energies, John Donoghue and other authors [30,31,32,33,34,35,36,37,38] have, along the years, established a solid prediction of the quantum corrections to the Schwarzschild field, and therefore to the Newtonian potential, at least at the first order in h. By comparing the effective Newtonian potential predicted by the ASG approach with the one computed in the framework of GR as an effective QFT, we arrive to establish, for the first time, a negative value for the parameter ω, unlike previous early predictions (see Refs. [11,22]).…”

Non-commutative Geometry from Perturbative Quantum Gravity

“…These invariant observables have been used to compute various effects in perturbative quantum gravity, such as quantum corrections to the Newtonian gravitational potential [34] or to the expansion rate of the early universe [35,36]. However, in this work, we are interested in the field-dependent coordinates X (µ) themselves.…”

“…) (which can be checked from ( 23) and ( 25)). Therefore, the middle two terms in (34) vanish and for the other two we can use the δ to perform the integral over s ′ and obtain…”

Strict deformations of quantum field theory in de Sitter spacetime

“…This method is an explicit example of the so-called geometrical clocks [15,16] used in the relational approach, and has the advantage that one can easily construct the fielddependent coordinates and corresponding relational observables to arbitrary order in perturbation theory. It has already been employed successfully in pQG for the computation of graviton loop corrections to invariant scalar correlators in Minkowski spacetime [12], of the quantum gravitational backreaction on the Hubble rate during inflation [17,18] and of quantum-gravity corrections to the Newtonian potential of a point particle [19].…”