Approaches to Quantum Gravity

526 F. Girelligroups, but also pushes for fundamental thinking about spacetime right at the intersectionbetween Special Relativity, General Relativity and Quantum Mechanics,the icing on the cake being the forthcoming experiments hopefully falsifying orconfirming the different approaches: a lot of excitement is coming up!AcknowledgementsI want to thank the Perimeter Institute for hospitality, where part of this work wasachieved. The content of this contribution has been shaped by discussions/workwith E. Livine, D. Oriti, and D. Poulin. I want also to thank L. Freidel, C. Rovelliand L. Smolin for inspiring discussions.References[1] S. Hossenfelder, The minimal length and large extra dimensions, Mod. Phys. Lett. A19 (2004) 2727, hep-ph/0410122.[2] L. Freidel, E. R. Livine, Ponzano–Regge model revisited III: Feynman diagrams andeffective field theory, hep-th/0502106.[3] G. Amelino-Camelia, L. Smolin, A. Starodubtsev, Quantum symmetry, thecosmological constant and Planck scale phenomenology, Class. Quant. Grav. 21(2004) 3095, hep-th/0306134.[4] F. Girelli, E. R. Livine, D. Oriti, Deformed Special Relativity as an effective flatlimit of quantum gravity, Nucl. Phys. B 708 (2005) 411–433, gr-qc/0406100[5] L. Freidel, J. Kowalski-Glikman, L. Smolin, 2+1 gravity and doubly specialrelativity, Phys. Rev. D 69 044001 (2004), hep-th/0307085.[6] H. Snyder, Quantized spacetime, Phys. Rev. Lett. 71 (1947) 38.[7] S. Liberati, S. Sonego, M. Visser, Interpreting doubly special relativity as a modifiedtheory of measurement, Phys. Rev. D 71 (2005) 045001, gr-qc/0410113.[8] R. Aloisio, A. Galante, A. F. Grillo, S. Liberati, E. Luzio, F. Mendez, Modifiedspecial relativity on a fluctuating spacetime, gr-qc/0607024.[9] S. Majid, H. Ruegg, Bicrossproduct structure of κ-Poincaré group andnon-commutative geometry, Phys. Lett. B 334 (1994) 348.[10] F. Girelli, S. Liberati, L. Sindoni, Planck-scale modified dispersion relations andFinsler geometry, gr-qc/0611024.[11] F. Girelli, T. Konopka, J. Kowalski-Glikman, E. R. Livine, The free particle indeformed special relativity, Phys. Rev. D 73 (2006) 045008, hep-th/0512107.[12] C. Rovelli, Partial observables, Phys. Rev. D 65 (2002) 124013, gr-qc/0110035.[13] B. Dittrich, Partial and complete observables for canonical general relativity,gr-qc/0507106.[14] L. Freidel, F. Girelli, E. R. Livine, The relativistic particle: Dirac observables andFeynman propagator, hep-th/0701113.[15] P. A. Dirac, Lectures on Quantum Mechanics (Dover Publications, 2001).[16] R. Arnowitt, S. Deser, C. W. Misner, The dynamics of General Relativity,gr-qc/0405109.[17] F. Girelli, D. Poulin, Quantum reference frame and deformation of the symmetries,in preparation.