On the correspondence between the classical and quantum gravity

TL;DR

This paper examines the relationship between classical and quantum gravity, showing discrepancies in potential definitions and providing a gauge-independent interpretation of loop corrections through the effective action.

Contribution

It demonstrates that the gravitational potential from scattering amplitudes conflicts with classical results and offers a gauge-invariant interpretation of quantum corrections using the effective action.

Findings

Discrepancy between quantum and classical gravitational potentials

Failure of scattering-based potential to describe non-Newtonian interactions

Gauge independence of one-loop radiative corrections

Abstract

The relationship between the classical and quantum theories of gravity is reexamined. The value of the gravitational potential defined with the help of the two-particle scattering amplitudes is shown to be in disagreement with the classical result of General Relativity given by the Schwarzschild solution. It is shown also that the potential so defined fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the $\hbar^0$-order part of the loop corrections is given directly in terms of the effective action. Gauge independence of that part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed.