Long-Range Behavior in Quantum Gravity

TL;DR

This paper investigates quantum gravity effects at low energies, analyzing how classical invariances are affected by quantum corrections, and explores long-range gravitational correlations and their implications for macroscopic bodies and black hole orbits.

Contribution

It establishes the violation of general covariance at one-loop order in quantum gravity and examines long-range properties of gravitational correlations using advanced formalisms.

Findings

One-loop quantum corrections violate classical general covariance.

The long-range two-point correlation function of gravity is finite outside particle localization.

Fluctuations of the Newton potential are quantified, with a relative RMS fluctuation of 1/√2.

Abstract

Quantum gravity effects of zeroth order in the Planck constant are investigated in the framework of the low-energy effective theory. A special emphasis is placed on establishing the correspondence between classical and quantum theories, for which purpose transformation properties of the \hbar^0-order radiative contributions to the effective gravitational field under deformations of a reference frame are determined. Using the Batalin-Vilkovisky formalism it is shown that the one-loop contributions violate the principle of general covariance, in the sense that the quantities which are classically invariant under such deformations take generally different values in different reference frames. In particular, variation of the scalar curvature under transitions between different reference frames is calculated explicitly. Furthermore, the long-range properties of the two-point correlation function of the gravitational field are examined. Using the Schwinger-Keldysh formalism it is proved that this function is finite in the coincidence limit outside the region of particle localization. In this limit, the leading term in the long-range expansion of the correlation function is calculated explicitly, and the relative value of the root mean square fluctuation of the Newton potential is found to be 1/\sqrt{2}. It shown also that in the case of a macroscopic gravitating body, the terms violating general covariance, and the field fluctuation are both suppressed by a factor 1/N, where N is the number of particles in the body. This leads naturally to a macroscopic formulation of the correspondence between classical and quantum theories of gravitation. As an application of the obtained results, the secular precession of a test particle orbit in the field of a black hole is determined.