Correspondence principle in quantum gravity

TL;DR

This paper examines the challenges of applying the correspondence principle in quantum gravity, critiques the traditional scattering amplitude approach, and proposes an effective action interpretation consistent with classical results and gauge invariance.

Contribution

It introduces an alternative interpretation of the correspondence principle using effective action and proves gauge independence of certain quantum corrections in scalar particles.

Findings

Traditional scattering approach conflicts with classical Schwarzschild solution.

Effective action provides a consistent framework for quantum gravity correspondence.

Gauge invariance of one-loop corrections is established.

Abstract

The problem of consistent formulation of the correspondence principle in quantum gravity is considered. The usual approach based on the use 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 this approach fails to describe whatever non-Newtonian interactions of macroscopic bodies. An alternative interpretation of the correspondence principle is given directly in terms of the effective action. Gauge independence of the \hbar^0 part of the one-loop radiative corrections to the gravitational form factors of the scalar particle is proved, justifying the interpretation proposed. Application to the black holes is discussed.