Manifestly Covariant Canonical Formalism of Quadratic Gravity

TL;DR

This paper develops a covariant quantization method for quadratic gravity, analyzing its physical modes, symmetries, and unitarity issues, and discusses potential ghost confinement to restore unitarity.

Contribution

It provides a manifestly covariant BRST quantization framework for quadratic gravity, including detailed commutation relations and analysis of physical content and unitarity.

Findings

Quadratic gravity has a massive scalar, ghost, and massless graviton as physical modes.

The theory is not unitary in its basic form.

Ghost confinement may restore unitarity of the S-matrix.

Abstract

We present the manifestly covariant quantization of quadratic gravity or higher-derivative gravity in the de Donder gauge condition (or harmonic gauge condition) for general coordinate invariance on the basis of the BRST transformation. We explicitly calculate various equal-time commutation relations (ETCRs), in particlular, the ETCRs between the metric tensor and its time derivatives in detail, and show that they are identically vanishing. We also clarify global symmetries, the physical content of quadratic gravity, and clearly show that this theory is not unitary and has a massive scalar, massive ghost and massless graviton as physical modes. Finally, we comment on confinement of the massive ghost, thereby recovering the unitarity of the physical S-matrix in quadratic gravity.