Introduction to Quantization of Conformal Gravity

TL;DR

This paper presents a consistent method for quantizing conformal gravity, addressing gauge fixing, ghost issues, and discontinuities, with insights into early quantization attempts and one-loop computations.

Contribution

It introduces a controllable quantization framework for conformal gravity, incorporating conformal gauge fixing and analyzing ghost and discontinuity issues.

Findings

Developed a covariant quantization approach for conformal gravity.

Identified challenges related to conformal gauge fixing and ghosts.

Provided explanations for first-loop quantum computations in conformal gravity.

Abstract

A method for consistent quantization of conformal gravity treating conformal symmetry in a very controllable way is presented. First, we discuss local conformal symmetry in the framework of gravitational interactions, where we view it as an example of a general gauge theory. We also present some early attempts at quantization of conformal gravity and use the generalized framework of covariant quantization due to Faddeev and Popov. Some salient issues such as the need for conformal gauge-fixing, an issue with conformal third ghosts, and discontinuities in conformal gravity are studied as well. Finally, we provide some explanations of the original ad hoc methods of computation valid at the first quantum loop level in conformal gravity.