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Approaches to Quantum Gravity

Approaches to Quantum Gravity

Approaches to Quantum Gravity

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Three-dimensional spin foam <strong>Quantum</strong> <strong>Gravity</strong> 309[12] L. Freidel, D. Louapre, Asymp<strong>to</strong>tics of 6j and 10j symbols, Class. Quant. Grav. 20(2003) 1267, hep-th/0209134.[13] A. M. Polyakov (Moscow, ITEP), Gauge Fields And Strings, Contempory Conceptsin Physics, 3 (Chur, Switzerland: Harwood, 1987).[14] D. Oriti, T. Tlas, Causality and matter propagation in 3d spin foam quantum gravity,Phys. Rev. D 74 (2006) 104021 [arXiv:gr-qc/0608116].[15] J. W. Barrett, I. Naish-Guzman, The Ponzano–Regge model and Reidemeister<strong>to</strong>rsion, arXiv:gr-qc/0612170.[16] A. Baratin, L. Freidel, Hidden quantum gravity in 3d Feynman diagrams,arXiv:gr-qc/0604016.[17] J. W. Barrett, Feynman diagams coupled <strong>to</strong> three-dimensional quantum gravity,Class. Quant. Grav. 23 (2006) 137 [arXiv:gr-qc/0502048].[18] L. Freidel, S. Majid, Noncommutative harmonic analysis, sampling theory and theDuflo map in 2+1 quantum gravity, arXiv:hep-th/0601004.[19] G. ’t Hooft, Quantization of space and time in 3 and in 4 space-time dimensions,arXiv:gr-qc/9608037.[20] S. Imai, N. Sasakura, Scalar field theories in a Lorentz-invariant three-dimensionalnoncommutative space-time, JHEP 0009 (2000) 032 [arXiv:hep-th/0005178].[21] G. t’Hooft, Non-perturbative 2 particle scattering amplitude in 2+1 dimensionalquantum gravity, Commun. Math. Phys. 117 (1988) 685700.[22] S. Deser, R. Jackiw, Classical and quantum scattering on a cone, Commun. Math.Phys. 118 (1988) 495509.[23] S. Carlip, Exact quantum scattering in (2+1)-dimensional gravity, Nucl. Phys. B324(1989) 106122.[24] F. A. Bais, N. M. Muller, B. J. Schroers, <strong>Quantum</strong> group symmetry and particlescattering in (2+1)-dimensional quantum gravity, Nucl. Phys. B 640, (2002) 3 ,hep-th/0205021.[25] R. Oeckl, Introduction <strong>to</strong> braided quantum field theory, Int. J. Mod. Phys. B 14(2000) 2461.[26] L. Freidel, A Ponzano–Regge model of Lorentzian 3-dimensional gravity, Nucl.Phys. Proc. Suppl. 88 (2000) 237–240, gr-qc/0102098.[27] S. Davids, A state sum model for (2+1) Lorentzian <strong>Quantum</strong> <strong>Gravity</strong>,gr-qc/0110114.[28] L. Freidel, E. R. Livine, Spin networks for non-compact groups, J. Math. Phys.44 (2003) 1322–1356, hep-th/0205268;[29] V. G. Turaev, O. Y. Viro, State sum invariants of 3 manifolds, and quantum {6 j}symbols, Topology 31 (1992) 865–902.[30] J. Kowalski-Glikman, Introduction <strong>to</strong> doubly special relativity (2004),hep-th/0405273.[31] H. Snyder, Quantized space-time, Phys.Rev. 71 (1947) 38.[32] A. Baratin, L. Freidel, Hidden quantum gravity in 4d Feynman diagrams:Emergence of spin foams (2006), arXiv:hep-th/0611042.[33] L. Freidel, A. Starodubtsev, <strong>Quantum</strong> gravity in terms of <strong>to</strong>pological observables,(2005), hep-th/0501191.

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