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Approaches to Quantum Gravity

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330 D. Oritiof the possibility of an hydrodynamic description could be tested in specific GFTmodels, and in very concrete and precise terms. A more detailed discussion of thepossible development of GFTs along these lines can be found in [44].Whether any of the above ideas will be realized, or other, not yet imagined,possibilities for development will become manifest in the near future, only furtherwork will tell. In our opinion, however, it is already clear that the GFT approachcan be the right framework for investigating the most fundamental questions about<strong>Quantum</strong> <strong>Gravity</strong>.References[1] D. Oriti, in: B. Fauser, J. Tolksdorf, E. Zeidler (eds.), <strong>Quantum</strong> <strong>Gravity</strong>(Birkhaeuser, 2006); gr-qc/0512103.[2] L. Freidel, Int. J. Theor. Phys. 44 (2005) 1769, hep-th/0505016.[3] S. Giddings, A. Strominger, Nucl. Phys. B 321 (1989) 481.[4] T Banks, Nucl. Phys. B 309 (1988) 493.[5] M. McGuigan, Phys. Rev. D 38 (1988) 3031.[6] J. C. Baez, J. W. Barrett, Adv. Theor. Math. Phys. 3 (1999) 815, gr-qc/9903060.[7] R. De Pietri, L. Freidel, K. Krasnov, C. Rovelli, Nucl. Phys. B 574 (2000) 785 ,hep-th/9907154.[8] J. W. Barrett, L. Crane, Class. Quant. Grav. 17 (2000) 3101, gr-qc/9904025.[9] D. Oriti, Rept. Prog. Phys. 64 (2001) 1489, gr-qc/0106091.[10] A. Perez, Class. Quant. Grav. 20 (2003) R43, gr-qc/0301113.[11] D. Oriti, J. Ryan, Hamil<strong>to</strong>nian analysis and Fock structure for generalised groupfield theories, in preparation.[12] A. Baratin, L. Freidel, E. Livine, Solving spin foam models: instan<strong>to</strong>ns and groupfield theory, in preparation.[13] M. Reisenberger, C. Rovelli, Class. Quant. Grav. 18 (2001) 121, gr-qc/0002095.[14] J. Ambjorn, J. Jurkiewicz, R. Loll, Phys. Rev. D 72 (2005) 064014, hep-th/0505154.[15] J. Ambjorn, B. Durhuus, T. Jonsson, Mod. Phys. Lett. A 6 (1991) 1133.[16] L. Freidel, D. Louapre, Nucl. Phys. B 662 (2003) 279, gr-qc/0212001.[17] R. De Pietri, C. Petronio, J. Math. Phys. 41 (2000) 6671, gr-qc/0004045.[18] A. Perez, C. Rovelli, Phys. Rev. D 63 (2001) 041501, gr-qc/0009021.[19] A. Perez, C. Rovelli, Phys. Rev. D 64 (2001) 064002, gr-qc/0011037.[20] E. Livine, A. Perez, C. Rovelli, Class. Quant. Grav. 20 (2003) 4425, gr-qc/0102051.[21] D. Oriti, C. Rovelli, S. Speziale, Class. Quant. Grav. 22 (2005) 85, gr-qc/0406063.[22] D. Boula<strong>to</strong>v, Mod. Phys. Lett. A 7 (1992) 1629, hep-th/9202074.[23] H. Ooguri, Mod. Phys. Lett. A 7 (1992) 2799, hep-th/9205090.[24] D. Oriti, Phys. Rev. D 73 (2006) 061502, gr-qc/0512069.[25] L. Freidel, D. Louapre, Phys. Rev. D 68 (2003) 104004, hep-th/0211026.[26] J. Halliwell, J. Hartle, Phys. Rev. D 43 (1991) 1170.[27] J. W. Barrett, R. M. Williams, Adv. Theor. Math. Phys. 3 (1999) 209, gr-qc/9809032.[28] E. Livine, D. Oriti, Nucl. Phys. B 663 (2003) 231, gr-qc/0210064.[29] D. Oriti, Phys. Rev. Lett. 94 (2005) 111301, gr-qc/0410134.[30] D. Oriti, Group field theory and simplicial quantum gravity, in preparation.[31] D. Oriti, T. Tlas, GFT and causal 3d spin foam models, in preparation.[32] K. Krasnov (2005), hep-th/0505174.

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