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Approaches to Quantum Gravity

Approaches to Quantum Gravity

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250 T. Thiemann[8] R. Brunetti, K. Fredenhagen, R. Verch, “The generally covariant locality principle: anew paradigm for local quantum field theory”, Commun. Math. Phys. 237 (2003)31–68, math-ph/0112041.[9] R. Wald, General Relativity (Chicago, The University of Chicago Press,1984).[10] M. Henneaux, C. Teitelboim, Quantization of Gauge Systems (Prince<strong>to</strong>n, Prince<strong>to</strong>nUniversity Press, 1992).[11] G. B. Folland, Harmonic Analysis in Phase Space, Ann. Math. Studies, no. 122,(Prince<strong>to</strong>n, Prince<strong>to</strong>n University Press, 1989).[12] T. Thiemann, “The Phoenix Project: master constraint programme for loop quantumgravity”, gr-qc/030580; “<strong>Quantum</strong> spin dynamics. VIII. The master constraint.”,gr-qc/0510011.[13] B. Dittrich, T. Thiemann, “Testing the master constraint programme for loopquantum gravity. I. General framework”, gr-qc/0411138; “II. Finite dimensionalsystems”, gr-qc/0411139; “III. SL(2,R) models”, gr-qc/0411140; “IV. Free fieldtheories”, gr-qc/0411141; “V. Interacting field theories”, gr-qc/0411142.[14] M. Reed, B. Simon, Methods of Modern Mathematical Physics, vol.2(NewYork,Academic Press, 1984).[15] B. Dittrich. “Partial and complete observables for Hamil<strong>to</strong>nian constrainedsystems”, gr-qc/0411013; “ Partial and complete observables for canonical generalrelativity”, gr-qc/0507106.[16] T. Thiemann, “Reduced phase space quantization and Dirac observables”,gr-qc/0411031.[17] A. Ashtekar, “New Hamil<strong>to</strong>nian formulation of General Relativity”, Phys. Rev. D36(1987) 1587–1602.[18] F. Barbero, “Real Ashtekar variables for Lorenzian signature space times”, Phys.Rev. D51 (1995) 5507–5510, gr-qc/9410014.[19] G. Immirzi, “<strong>Quantum</strong> gravity and Regge calculus”, Nucl. Phys. Proc. Suppl. 57(1997) 65, gr-qc/9701052.[20] C. Rovelli, T. Thiemann, “The Immirzi parameter in quantum General Relativity”,Phys. Rev. D57 (1998) 1009–1014, gr-qc/9705059.[21] J. Lewandowski, A. Okolow, H. Sahlmann, T. Thiemann, “Uniqueness ofdiffeomorphism invariant states on holonomy–flux algebras”, gr-qc/0504147.[22] A. Ashtekar, C.J. Isham, “Representations of the holonomy algebras of gravityand non-Abelian gauge theories”, Class. <strong>Quantum</strong> Grav. 9 (1992) 1433,hep-th/9202053.[23] A. Ashtekar, J. Lewandowski, “Representation theory of analytic Holonomy C ⋆algebras”, in Knots and <strong>Quantum</strong> <strong>Gravity</strong>, J. Baez (ed.) (Oxford, Oxford UniversityPress, 1994).[24] A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, T. Thiemann, “Quantization fordiffeomorphism invariant theories of connections with local degrees of freedom”,Journ. Math. Phys. 36 (1995) 6456–6493, gr-qc/9504018.[25] T. Thiemann, “Anomaly-free formulation of non-perturbative, four-dimensionalLorentzian quantum gravity”, Physics Letters B380 (1996) 257–264,gr-qc/9606088[26] T. Thiemann, “<strong>Quantum</strong> spin dynamics (QSD)”, Class. <strong>Quantum</strong> Grav. 15 (1998)839–873, gr-qc/9606089.[27] T. Thiemann, “<strong>Quantum</strong> spin dynamics (QSD) II. The kernel of theWheeler–DeWitt constraint opera<strong>to</strong>r”, Class. <strong>Quantum</strong> Grav. 15 (1998) 875–905,gr-qc/9606090.

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