Classical and Quantum Gravity on Conformal Superspace

TL;DR

This paper explores a new formulation of gravity theories based on conformal superspace, which simplifies canonical quantization and offers more predictive power compared to traditional approaches.

Contribution

It introduces a gravity framework on conformal superspace, reducing complexities in quantization and enhancing the theory's predictive capabilities.

Findings

New symmetry is more restrictive and predictive.

Many canonical quantization difficulties are alleviated.

Provides a novel approach to quantum gravity theories.

Abstract

The four-dimensional gauge group of general relativity corresponds to arbitrary coordinate transformations on a four-manifold. Theories of gravity with a dynamical structure remarkably like Einstein's theory can be obtained on the basis of a four-dimensional gauge group of arbitrary coordinate and conformal transformations of riemannian metrics defined on a three-manifold. This new symmetry is more restrictive and hence more predictive. Many of the difficulties that have plagued the canonical quantization of general relativity seem to vanish.