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 hμν of the metric, a massive scalar ϕ and the spin-2 fakeon χμν . The fields ϕ and χμν are introduced explicitly at the level of the Lagrangian by means of standard procedures. We consider two options, where ϕ 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 χμν , 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 χμν is a ghost instead of a fakeon.

Highlights

  • Derivatives and is organized so as to fully diagonalize the kinetic part in the nonlinear case

  • Quantum gravity is described by a graviton multiplet, made of the fluctuation hμν of the metric tensor around flat space, a massive scalar φ and a massive spin-2 field χμν

  • We have studied various aspects of the theory of quantum gravity proposed in ref. [1], after converting its higher-derivative action into an action with two-derivative kinetic terms

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Summary

Isolating the fakeons in quantum gravity

The theory of quantum gravity (coupled to matter) proposed in ref. [1] has action. where α, ξ, ζ, ΛC and κ are real constants, with α > 0, ξ > 0 and ζ > 0, and Sm is the action of the matter sector. The theory of quantum gravity (coupled to matter) proposed in ref. We obtain an equivalent action that does not contain higher-derivatives and is useful for the calculations of the sections. We explain how to quantize the theory in the new setting. The authors of [15] work at ΛC = 0, with no matter sector Sm and stop short of finalizing the action to concentrate on the analysis of the quadratic part around flat space, since their main interest is to highlight the degrees of freedom. We assume that Sm is at least quadratic in the matter fields Φ. And adding the integral of a total derivative, the action (2.1) can be written in the more convenient form.

Step 2: spin-2 fakeon
Quantization
Absorptive part of the self-energy
The fakeon width
Comparison with the Stelle theory
Conclusions
A Calculations of absorptive parts
B Contributions of Proca and Pauli-Fierz fields
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