Fakeons, unitarity, massive gravitons and the cosmological constant

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.

arXiv comment33 pages, 2 figures; v2: minor changes, JHEP

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• On the Perturbative Quantization of Einstein-Hilbert Gravity Embedded in a Higher Derivative Model
• Black Hole Remnants from Dynamical Dimensional Reduction?
• Purely virtual extension of quantum field theory for gauge invariant fields: Yang-Mills theory
• Gauge theories and quantum gravity in a finite interval of time, on a compact space manifold