Higher-Derivative Quantum Gravity with Purely Virtual Particles: Renormalizability and Unitarity

TL;DR

This paper discusses a novel approach to higher-derivative quantum gravity using purely virtual particles, achieving a renormalizable and unitary theory by eliminating ghost states and exploring cosmological implications.

Contribution

It introduces the concept of purely virtual particles in quantum field theories and demonstrates their role in resolving ghosts in higher-derivative quantum gravity.

Findings

Achieves a renormalizable and unitary higher-derivative quantum gravity theory.

Develops spectral identities crucial for proving unitarity.

Explores phenomenological consequences in inflationary cosmology.

Abstract

We review the formulation of quantum field theories with purely virtual particles, a new type of degrees of freedom that can mediate interactions without ever appear as external on-shell states. This property allows to solve the problem of ghosts in higher-derivative quantum gravity, leading to a renormalizable and unitary theory. The main steps for the BRST quantization of gravity are recalled and renormalizability is discussed. Then, we introduce purely virtual particles in a general quantum field theory and show the derivation of the so-called spectral identities, which are a key ingredient to prove unitarity. Finally, phenomenological consequences and predictions in inflationary cosmology are presented.