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 Λ. The scattering amplitudes, defined by expanding the metric around flat space, obey the optical theorem up to corrections due to Λ, 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.

Quantum field theory of physical and purely virtual particles in a finite interval of time on a compact space manifold: diagrams, amplitudes and unitarity

“…In the case of purely virtual particles, where no symmetry is helping us, we need to make the surgical operation described above, on the internal sectors of the diagrams, which amounts to dropping the delta functions with ωpv-dependent supports. Applied to gauge theories, the prescription/projection operations return the same physical results we obtain with the usual quantization method [49].…”

A new quantization principle from a minimally non time-ordered product

“…Applying the map V → V ph (A) to that case, we recover the proof of unitarity in gauge theories given in ref. [26].…”

Fakeons and microcausality: light cones, gravitational waves and the Hubble constant

“…It provides a better understanding of the Lee-Wick models [3,4], overcoming ambiguities [5] and problems with Lorentz invariance [6], and actually leading to the completion of their formulation [7]. Moreover, fakeons allow us to simplify the proofs of perturbative unitarity in gauge and gravity theories [8]. But their most important application is that they lead to a consistent, and basically unique, theory of quantum gravity [1,9,10].…”