Limiting fluctuations in quantum gravity to diffeomorphisms

TL;DR

This paper demonstrates that constraining quantum fluctuations to diffeomorphisms in quantum gravity leads to a theory with no quantum corrections, effectively making it finite, unitary, and background independent.

Contribution

It introduces a novel approach where limiting fluctuations to gauge transformations results in a renormalization-free, background-independent quantum gravity theory.

Findings

Quantum corrections vanish on shell when fluctuations are limited to diffeomorphisms.

The resulting theory is finite and requires no renormalization.

This approach establishes a link between background independence and renormalizability.

Abstract

Within the background field formalism of quantum gravity, I show that if the quantum fluctuations are limited to diffeomorphic gauge transformations rather than the physical degrees of freedom, as in conventional quantum field theory, all the quantum corrections vanish on shell and the effective action is equivalent to the classical action. In principle, the resulting theory is finite and unitary, and requires no renormalization. I also show that this is the unique parameterization that renders the path integral independent of the on-shell condition for the background field, a form of background independence. Thus, a connection is established between background independence and renormalizability and unitarity.