Kawai, Hikaru; Kitazawa, Yoshihisa; Ninomiya, Masao Renormalizability of quantum gravity near two dimensions. (English) Zbl 1002.81519 Nucl. Phys., B 467, No. 1-2, 313-331 (1996). Summary: We study the renormalizability of quantum gravity near two dimensions. Our formalism starts with the tree action which is invariant under the volume preserving diffeomorphism. We identify the BRS invariance which originates from full diffeomorphism invariance. We study the Ward-Takahashi identities to determine the general structure of the counter terms. We prove to all orders that the counter terms can be supplied by the coupling and the wave function renormalization of the tree action. The bare action can be constructed to be of the Einstein action form which ensures full diffeomorphism invariance. Cited in 9 Documents MSC: 81T15 Perturbative methods of renormalization applied to problems in quantum field theory 81T40 Two-dimensional field theories, conformal field theories, etc. in quantum mechanics 83C45 Quantization of the gravitational field Keywords:volume preserving diffeomorphism; Ward Takahashi identities; wave function renormalization; Einstein action form; near two dimensions PDFBibTeX XMLCite \textit{H. Kawai} et al., Nucl. Phys., B 467, No. 1--2, 313--331 (1996; Zbl 1002.81519) Full Text: DOI arXiv References: [1] Christensen, S. M.; Duff, M. J., Phys. Lett. B, 79, 213 (1978) [2] Kawai, H.; Ninomiya, M., Nucl. Phys. B, 336, 115 (1990) [3] Kawai, H.; Ninomiya, M., Nucl. Phys. B, 393, 280 (1993) [4] Kawai, H.; Kitazawa, Y.; Ninomiya, M., Nucl. Phys. B, 404, 684 (1993) [5] Aida, T.; Kitazawa, Y.; Kawai, H.; Ninomiya, M., Nucl. Phys. B, 427, 158 (1994) [6] Aida, T.; Kitazawa, Y.; Nishimura, J.; Tsuchiya, A., Nucl. Phys. B, 444, 353 (1995) [7] Kitazawa, Y., Nucl. Phys. B, 453, 477 (1995) [8] Zinn-Justin, J., Quantum field theory and critical phenomena (1989), Oxford Univ. Press: Oxford Univ. Press Oxford, Section 21 [9] Knizhnik, V. G.; Polyakov, A. M.; Zamolodchikov, A. B., Mod. Phys. Lett. A, 3, 819 (1988) [10] Distler, J.; Kawai, H., Nucl. Phys. B, 321, 504 (1989) [11] Klebanov, I. R.; Kogan, I. I.; Polyakov, A. M., Phys. Rev. Lett., 71, 3243 (1993) [12] G. Bamich, F. Brandt and M. Henneaux, Local BRST cohomology in Einstein-Yang-Mills theory, preprint KUL-TF-95/16,ULB-TH-95/07, hep-th/9505173.; G. Bamich, F. Brandt and M. Henneaux, Local BRST cohomology in Einstein-Yang-Mills theory, preprint KUL-TF-95/16,ULB-TH-95/07, hep-th/9505173. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.