Quantum Gravity, Fakeons And Microcausality

TL;DR

This paper explores the properties of fakeons in quantum gravity at one loop, analyzing causality violations at high energies and comparing fakeons with ghosts in the context of quantum gravitational theories.

Contribution

It introduces a detailed analysis of fakeons in quantum gravity, including their impact on causality and comparison with ghost fields in Stelle theory.

Findings

Fakeons cause causality violations at energies above their mass.

The width of the fakeon indicates negative values, affecting unitarity.

Comparison shows differences between fakeons and ghosts in quantum gravity.

Abstract

We investigate the properties of fakeons in quantum gravity at one loop. The theory is described by a graviton multiplet, which contains the fluctuation $h_{\mu \nu }$ of the metric, a massive scalar $\phi $ and the spin-2 fakeon $\chi _{\mu \nu }$. The fields $\phi $ and $\chi _{\mu \nu }$ are introduced explicitly at the level of the Lagrangian by means of standard procedures. We consider two options, where $\phi $ is quantized as a physical particle or a fakeon, and compute the absorptive part of the self-energy of the graviton multiplet. The width of $\chi _{\mu \nu }$, which is negative, shows that the theory predicts the violation of causality at energies larger than the fakeon mass. We address this issue and compare the results with those of the Stelle theory, where $\chi _{\mu \nu }$ is a ghost instead of a fakeon.