On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model II

TL;DR

This paper details the perturbative quantization of Einstein-Hilbert gravity within a higher derivative framework, analyzing field decomposition, unitarity, and renormalization properties, with implications for quantum gravity theories.

Contribution

It provides a detailed decomposition of the gravitational field into massless and massive components and explores the renormalization and unitarity properties in a higher derivative gravity model.

Findings

Massive fields lack poles at higher orders, indicating no particle states.

Tree-level unitarity is violated, but higher-order corrections do not.

Finiteness properties simplify renormalization group analysis.

Abstract

In a previous paper we presented the renormalization of Einstein-Hilbert gravity under inclusion of higher derivative terms and proposed a projection down to the physical state space of Einstein-Hilbert. In the present paper we describe this procedure in more detail via decomposing the original double-pole field $h^{\mu\nu}$ in the bilinear field sector into a massless and a massive spin two field. Those are associated with the poles at zero mass resp. at non-zero mass of $h$ in the tree approximation. We show that the massive fields have no poles in higher orders hence do not correspond to particles. $S$-matrix unitarity is violated only in tree approximation. On the way to these results we derive finiteness properties which are valid in the Landau gauge. Those simplify the renormalization group analysis of the model considerably. We also establish a rigid Weyl identity which represents a proper substitute for a Callan-Symanzik equation in flat spacetime.