Fakeons, unitarity, massive gravitons and the cosmological constant

TL;DR

This paper proves perturbative unitarity in gauge theories and quantum gravity using a special gauge and fakeon prescription, clarifies scattering with a cosmological constant, and constructs local, unitary massive graviton theories.

Contribution

It introduces a simple proof of unitarity in quantum gravity with fakeons and clarifies the effects of a cosmological constant on scattering amplitudes.

Findings

Perturbative unitarity holds with the fakeon prescription.

Scattering amplitudes obey the optical theorem with negligible corrections from .

Constructed local, unitary theories of massive gravitons and gauge fields.

Abstract

We give a simple proof of perturbative unitarity in gauge theories and quantum gravity using a special gauge that allows us to separate the physical poles of the free propagators, which are quantized by means of the Feynman prescription, from the poles that belong to the gauge-trivial sector, which are quantized by means of the fakeon prescription. The proof applies to renormalizable theories, including the ultraviolet complete theory of quantum gravity with fakeons formulated recently, as well as low-energy (nonrenormalizable) theories. We clarify a number of subtleties related to the study of scattering processes in the presence of a cosmological constant $\Lambda$. The scattering amplitudes, defined by expanding the metric around flat space, obey the optical theorem up to corrections due to $\Lambda$, which are negligible for all practical purposes. Problems of interpretation would arise if such corrections became important. In passing, we obtain local, unitary (and "almost" renormalizable) theories of massive gravitons and gauge fields, which violate gauge invariance and general covariance explicitly.