Conformal Transformations and Quantum Gravity

TL;DR

This paper explores how quantum effects of matter relate to conformal transformations in spacetime, comparing scale and conformal changes, and advocates for scalar-tensor theories as a promising framework for quantum gravity.

Contribution

It investigates the equivalence of quantum effects via scale and conformal transformations and proposes scalar-tensor theories as the ideal foundation for quantum gravity.

Findings

Quantum effects can be represented through conformal degrees of freedom.

Scale and conformal transformations offer equivalent descriptions of quantum effects.

Scalar-tensor theories are suitable for formulating quantum gravity.

Abstract

Recently\cite{BQG}, it was shown that quantum effects of matter could be identified with the conformal degree of freedom of the space-time metric. Accordingly, one can introduce quantum effects either by making a scale transformation (i.e. changing the metric), or by making a conformal transformation (i.e. changing all physical quantities). These two ways are investigated and compared. Also, it is argued that, the ultimate formulation of such a quantum gravity theory should be in the framework of the scalar-tensor theories.