Abstract
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons. The classical Lagrangian contains the cosmological term, the Hilbert term, sqrt{-g}{R}_{mu nu }{R}^{mu nu } and sqrt{-g}{R}^2 . In this paper, we compute the one-loop renormalization of the theory and the absorptive part of the graviton self energy. The results illustrate the mechanism that makes renormalizability compatible with unitarity. The fakeons disentangle the real part of the self energy from the imaginary part. The former obeys a renormalizable power counting, while the latter obeys the nonrenormalizable power counting of the low energy expansion and is consistent with unitarity in the limit of vanishing cosmological constant. The value of the absorptive part is related to the central charge c of the matter fields coupled to gravity.
Highlights
A theory of quantum gravity has been recently proposed by means of a novel quantization prescription, which is able to turn the poles of the free propagators that are due to the higher derivatives into fakeons
We quantize the theory with the help of the BatalinVilkovisky formalism [21,22,23] and calculate the divergences of the graviton self energy and those of the diagrams that renormalize the symmetry transformations of the fields
In this paper we have studied the theory of quantum gravity proposed in ref. [1], by computing its renormalization at one loop and the absorptive part of the graviton self energy
Summary
We skip this part for the time being, because we want to concentrate on the one-loop renormalization, which coincides with the one of the Euclidean version of the theory [1, 2]. SK = − Rα(Φ)Kα = (gμρ∂ν Cρ+gνρ∂μCρ+Cρ∂ρgμν )Kμν + Cσ(∂σCρ)KρC − BσKσCcollects the infinitesimal symmetry transformations Rα(Φ) of the fields, coupled to the sources Kα. = Rμν (g, C) ≡ −gμρ∂ν Cρ − gνρ∂μCρ − Cρ∂ρgμν are inherited from the infinitesimal transformations δΣgμν = Rμν(g, Σ) of the metric tensor gμν under diffeomorphisms, where Σρ are functions of the spacetime point. The indices of ∂μ, hμν, the fields Φα (except gμν) and the sources Kα are raised and lowered by means of the flat-space metric. The ghost actions (2.8) and (2.9) are equivalent for our purposes of this paper
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