On the quantum field theory of the gravitational interactions
- 119 Downloads
We study the main options for a unitary and renormalizable, local quantum field theory of the gravitational interactions. The first model is a Lee-Wick superrenormalizable higher-derivative gravity, formulated as a nonanalytically Wick rotated Euclidean theory. We show that, under certain conditions, the S matrix is unitary when the cosmological constant vanishes. The model is the simplest of its class. However, infinitely many similar options are allowed, which raises the issue of uniqueness. To deal with this problem, we propose a new quantization prescription, by doubling the unphysical poles of the higher-derivative propagators and turning them into Lee-Wick poles. The Lagrangian of the simplest theory of quantum gravity based on this idea is the linear combination of R, R μν R μν , R 2 and the cosmological term. Only the graviton propagates in the cutting equations and, when the cosmological constant vanishes, the S matrix is unitary. The theory satisfies the locality of counterterms and is renormalizable by power counting. It is unique in the sense that it is the only one with a dimensionless gauge coupling.
KeywordsModels of Quantum Gravity Beyond Standard Model Renormalization Regularization and Renormalons
This article is distributed under the terms of the Creative Commons Attribution License (CC-BY 4.0), which permits any use, distribution and reproduction in any medium, provided the original author(s) and source are credited.
- G. ’t Hooft and M. Veltman, One-loop divergences in the theory of gravitation, Ann. Inst. H. Poincaré Phys. Theor. A 20 (1974) 69.Google Scholar
- S. Weinberg, Ultraviolet divergences in quantum theories of gravitation, in An Einstein centenary survey, S. Hawking and W. Israel eds., Cambridge University Press, Cambridge U.K. (1979), pg. 790.Google Scholar
- Yu.V. Kuz’min, Finite nonlocal gravity, Sov. J. Nucl. Phys. 50 (1989) 6 [Yad. Fiz. 50 (1989) 1630].Google Scholar
- G. ’t Hooft, Renormalization of massless Yang-Mills fields, Nucl. Phys. B 33 (1971) 173 [INSPIRE].
- G. ’t Hooft, Renormalizable Lagrangians for massive Yang-Mills fields, Nucl. Phys. B 35 (1971) 167 [INSPIRE].