Analysis of Unitarity in Conformal Quantum Gravity

TL;DR

This paper investigates the unitarity of quantum conformal gravity through canonical quantization, revealing violations in unitarity during scattering processes and offering new insights into the ghost problem in quadratic gravity theories.

Contribution

It provides a detailed canonical quantization of Weyl's conformal gravity and analyzes the unitarity of the resulting quantum theory, highlighting issues with the physical subspace.

Findings

Unitarity is violated in scattering events within the quantum conformal gravity framework.

The physical subspace has an indefinite inner product metric and a single eigenstate Hamiltonian.

The study offers a new perspective on the ghost problem in quadratic quantum gravity theories.

Abstract

We perform a canonical quantization of Weyl's conformal gravity by means of the covariant operator formalism and investigate the unitarity of the resulting quantum theory. After reducing the originally fourth order theory to second order in time derivatives via the introduction of an auxiliary tensor field, we identify the full Fock space of quantum states under a BRST construction that includes Faddeev-Popov ghost fields corresponding to Weyl transformations. Using the Kugo-Ojima quartet mechanism, we identify the physical subspace of quantum states and find that the subspace containing the transverse spin-2 states comes equipped with an indefinite inner product metric and a one-particle Hamiltonian that possesses only a single eigenstate. We construct the LSZ reduction formula for the S-matrix in this spin-2 subspace and find that unitarity is violated in scattering events. The explicit way in which this violation occurs represents a new view on the ghost-problem in quadratic theories of quantum gravity.