1. C. Rovelli, Quantum Gravity, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2004). doi:10.1017/CBO9780511755804.
  2. C. Rovelli and F. Vidotto, Covariant Loop Quantum Gravity: An Elementary Introduction to Quantum Gravity and Spinfoam Theory, Cambridge Monographs on Mathematical Physics (Cambridge University Press, 2014). doi:10.1017/CBO9781107706910.
  3. T. Thiemann, Modern Canonical Quantum General Relativity (Cambridge University Press, 2007). arXiv:gr-qc/0110034. doi:10.1017/CBO9780511755682.
  4. J. D. Bekenstein, “Black holes and entropy,” Phys. Rev. D 7, 2333 (1973). doi:10.1103/PhysRevD.7.2333.
  5. S. W. Hawking, “Particle creation by black holes,” Commun. Math. Phys. 43, 199 (1975). doi:10.1007/BF02345020.
  6. M. . J. . G. Veltman, “One-loop divergencies in the theory of gravitation,” Ann. Inst. H. Poincaré Phys. Théor. A 20, 69 (1974).
  7. M. H. Goroff and A. Sagnotti, “The ultraviolet behavior of Einstein gravity,” Nucl. Phys. B 266, 709 (1986). doi:10.1016/0550-3213(86)90193-8.
  8. A. Ashtekar, “New variables for classical and quantum gravity,” Phys. Rev. Lett. 57, 2244 (1986). doi:10.1103/PhysRevLett.57.2244.
  9. A. Ashtekar, “New Hamiltonian formulation of general relativity,” Phys. Rev. D 36, 1587 (1987). doi:10.1103/PhysRevD.36.1587.
  10. J. . F. Barbero\bibnamedelima G., “Real Ashtekar variables for Lorentzian signature space-times,” Phys. Rev. D 51, 5507 (1995). arXiv:gr-qc/9410014. doi:10.1103/PhysRevD.51.5507.
  11. S. Holst, “Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action,” Phys. Rev. D 53, 5966 (1996). arXiv:gr-qc/9511026. doi:10.1103/PhysRevD.53.5966.
  12. G. Immirzi, “Quantum gravity and Regge calculus,” Nucl. Phys. B Proc. Suppl. 57, 65 (1997). arXiv:gr-qc/9701052. doi:10.1016/S0920-5632(97)00354-X.
  13. G. Immirzi, “Real and complex connections for canonical gravity,” Class. Quantum Grav. 14, L177 (1997). arXiv:gr-qc/9612030. doi:10.1088/0264-9381/14/10/002.
  14. R. Arnowitt, S. Deser and C. W. Misner, “Dynamical structure and definition of energy in general relativity,” Phys. Rev. 116, 1322 (1959). doi:10.1103/PhysRev.116.1322.
  15. R. Arnowitt, S. Deser and C. W. Misner, “The dynamics of general relativity,” Gen. Relativ. Gravit. 40, 1997 (2008). arXiv:gr-qc/0405109. doi:10.1007/s10714-008-0661-1.
  16. T. Jacobson and L. Smolin, “Nonperturbative quantum geometries,” Nucl. Phys. B 299, 295 (1988). doi:10.1016/0550-3213(88)90286-6.
  17. C. Rovelli and L. Smolin, “Loop space representation of quantum general relativity,” Nucl. Phys. B 331, 80 (1990). doi:10.1016/0550-3213(90)90019-A.
  18. R. Penrose, “Angular momentum: an approach to combinatorial space-time,” in Quantum Theory and Beyond, edited by T. Bastin (Cambridge University Press, 1971), pp. 151\bibrangedash 180.
  19. C. Rovelli and L. Smolin, “Spin networks and quantum gravity,” Phys. Rev. D 52, 5743 (1995). arXiv:gr-qc/9505006. doi:10.1103/PhysRevD.52.5743.
  20. C. Rovelli and L. Smolin, “Discreteness of area and volume in quantum gravity,” Nucl. Phys. B 442, 593 (1995). arXiv:gr-qc/9411005. doi:10.1016/0550-3213(95)00150-Q.
  21. A. Ashtekar and J. Lewandowski, “Quantum theory of geometry: I. Area operators,” Class. Quantum Grav. 14, A55 (1997). arXiv:gr-qc/9602046. doi:10.1088/0264-9381/14/1A/006.
  22. A. Ashtekar and J. Lewandowski, “Quantum theory of geometry II: Volume operators,” Adv. Theor. Math. Phys. 1, 388 (1997). arXiv:gr-qc/9711031. doi:10.4310/ATMP.1997.v1.n2.a8.
  23. T. Thiemann, “Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity,” Phys. Lett. B 380, 257 (1996). arXiv:gr-qc/9606088. doi:10.1016/0370-2693(96)00532-1.
  24. T. Thiemann, “Quantum spin dynamics (QSD),” Class. Quantum Grav. 15, 839 (1998). arXiv:gr-qc/9606089. doi:10.1088/0264-9381/15/4/011.
  25. M. P. Reisenberger and C. Rovelli, “`Sum over surfaces' form of loop quantum gravity,” Phys. Rev. D 56, 3490 (1997). arXiv:gr-qc/9612035. doi:10.1103/PhysRevD.56.3490.
  26. J. C. Baez, “Spin foam models,” Class. Quantum Grav. 15, 1827 (1998). arXiv:gr-qc/9709052. doi:10.1088/0264-9381/15/7/004.
  27. A. Perez, “The spin-foam approach to quantum gravity,” Living Rev. Relativ. 16, 3 (2013). arXiv:1205.2019. doi:10.12942/lrr-2013-3.
  28. J. Engle, E. Livine, R. Pereira and C. Rovelli, “LQG vertex with finite Immirzi parameter,” Nucl. Phys. B 799, 136 (2008). arXiv:0711.0146. doi:10.1016/j.nuclphysb.2008.02.018.
  29. L. Freidel and K. Krasnov, “A new spin foam model for 4D gravity,” Class. Quantum Grav. 25, 125018 (2008). arXiv:0708.1595. doi:10.1088/0264-9381/25/12/125018.
  30. C. Rovelli, “Black hole entropy from loop quantum gravity,” Phys. Rev. Lett. 77, 3288 (1996). arXiv:gr-qc/9603063. doi:10.1103/PhysRevLett.77.3288.
  31. A. Ashtekar, J. Baez, A. Corichi and K. Krasnov, “Quantum geometry and black hole entropy,” Phys. Rev. Lett. 80, 904 (1998). arXiv:gr-qc/9710007. doi:10.1103/PhysRevLett.80.904.
  32. M. Bojowald, “Absence of a singularity in loop quantum cosmology,” Phys. Rev. Lett. 86, 5227 (2001). arXiv:gr-qc/0102069. doi:10.1103/PhysRevLett.86.5227.
  33. A. Ashtekar, T. Pawlowski and P. Singh, “Quantum nature of the big bang,” Phys. Rev. Lett. 96, 141301 (2006). arXiv:gr-qc/0602086. doi:10.1103/PhysRevLett.96.141301.
  34. E. Frodden, A. Ghosh and A. Perez, “Quasilocal first law for black hole thermodynamics,” Phys. Rev. D 87, 121503 (2013). arXiv:1110.4055. doi:10.1103/PhysRevD.87.121503.
  35. P. Doná and S. Speziale, “Introductory lectures to loop quantum gravity,” in Gravitation : Théorie et Expérience, edited by A. Bounames and A. Makhlouf (Hermann, 2013), pp. 89\bibrangedash 140. arXiv:1007.0402.
  36. A. Perez, “Introduction to loop quantum gravity and spin foams” (2004). arXiv:gr-qc/0409061.
  37. C. Rovelli, “Loop quantum gravity,” Living Rev. Relativ. 11, 5 (2008). doi:10.12942/lrr-2008-5.
  38. A. Ashtekar and J. Lewandowski, “Background independent quantum gravity: a status report,” Class. Quantum Grav. 21, R53 (2004). arXiv:gr-qc/0404018. doi:10.1088/0264-9381/21/15/R01.
  39. M. Nakahara, Geometry, Topology and Physics (Institute of Physics Publishing, 2003).
  40. R. M. Wald, General Relativity (University of Chicago Press, 1984). doi:10.7208/chicago/9780226870373.001.0001.
  41. P. A. . M. Dirac, Lectures on Quantum Mechanics, Belfer Graduate School of Science Monographs Series (Belfer Graduate School of Science, Yeshiva University, 1964).
  42. H. . T. Nieh and M. . L. Yan, “An identity in Riemann-Cartan geometry,” J. Math. Phys. 23, 373 (1982). doi:10.1063/1.525379.
  43. L. Freidel, D. Minic and T. Takeuchi, “Quantum gravity, torsion, parity violation, and all that,” Phys. Rev. D 72, 104002 (2005). arXiv:hep-th/0507253. doi:10.1103/PhysRevD.72.104002.
  44. A. Perez and C. Rovelli, “Physical effects of the Immirzi parameter in loop quantum gravity,” Phys. Rev. D 73, 044013 (2006). arXiv:gr-qc/0505081. doi:10.1103/PhysRevD.73.044013.
  45. P. A. . M. Dirac, “Generalized Hamiltonian dynamics,” Can. J. Math. 2, 129 (1950). doi:10.4153/CJM-1950-012-1.
  46. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, 1992).
  47. B. S. DeWitt, “Quantum theory of gravity. I. The canonical theory,” Phys. Rev. 160, 1113 (1967). doi:10.1103/PhysRev.160.1113.
  48. J. A. Wheeler, “Superspace and the nature of quantum geometrodynamics,” in Battelle Rencontres, edited by C. M. DeWitt and J. A. Wheeler (W. A. Benjamin, 1968), pp. 242\bibrangedash 307.
  49. É. Gourgoulhon, 3+1 Formalism in General Relativity: Bases of Numerical Relativity, Lecture Notes in Physics (Springer, 2012). arXiv:gr-qc/0703035. doi:10.1007/978-3-642-24525-1.
  50. A. Peres, “On Cauchy's problem in general relativity – II,” Nuovo Cimento 26, 53 (1962). doi:10.1007/BF02754342.
  51. C. Rovelli and T. Thiemann, “Immirzi parameter in quantum general relativity,” Phys. Rev. D 57, 1009 (1998). arXiv:gr-qc/9705059. doi:10.1103/PhysRevD.57.1009.
  52. R. Gambini and J. Pullin, Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge University Press, 1996). doi:10.1017/CBO9780511524431.
  53. R. Gambini and J. Pullin, A First Course in Loop Quantum Gravity (Oxford University Press, 2011). doi:10.1093/acprof:oso/9780199590759.001.0001.
  54. R. Giles, “Reconstruction of gauge potentials from Wilson loops,” Phys. Rev. D 24, 2160 (1981). doi:10.1103/PhysRevD.24.2160.
  55. S. Mandelstam, “Feynman rules for electromagnetic and Yang-Mills fields from the gauge-independent field-theoretic formalism,” Phys. Rev. 175, 1580 (1968). doi:10.1103/PhysRev.175.1580.
  56. A. Ashtekar and J. Lewandowski, “Representation theory of analytic holonomy C∗C^*-algebras,” in Knots and Quantum Gravity, edited by J. C. Baez (Oxford University Press, 1994), pp. 21\bibrangedash 61. arXiv:gr-qc/9311010. doi:10.1093/oso/9780198534907.003.0002.
  57. J. Lewandowski, H. Sahlmann and T. Thiemann, “Uniqueness of diffeomorphism invariant states on holonomy-flux algebras,” Commun. Math. Phys. 267, 703 (2006). arXiv:gr-qc/0504147. doi:10.1007/s00220-006-0100-7.
  58. C. Fleischhack, “Representations of the Weyl algebra in quantum geometry,” Commun. Math. Phys. 285, 67 (2009). arXiv:math-ph/0407006. doi:10.1007/s00220-008-0593-3.
  59. R. Loll, “Spectrum of the volume operator in quantum gravity,” Nucl. Phys. B 460, 143 (1996). arXiv:gr-qc/9511030. doi:10.1016/0550-3213(95)00627-3.
  60. B. Dittrich and T. Thiemann, “Are the spectra of geometrical operators in loop quantum gravity really discrete?,” J. Math. Phys. 50, 012503 (2009). arXiv:0708.1721. doi:10.1063/1.3054277.
  61. E. Bianchi, P. Doná and S. Speziale, “Polyhedra in loop quantum gravity,” Phys. Rev. D 83, 044035 (2011). arXiv:1009.3402. doi:10.1103/PhysRevD.83.044035.
  62. A. Ashtekar, “Loop quantum gravity: four recent advances and a dozen frequently asked questions,” in The Eleventh Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories, edited by H. Kleinert, R. T. Jantzen and R. Ruffini (World Scientific, 2008), pp. 126\bibrangedash 147. arXiv:0705.2222. doi:10.1142/9789812834300_0008.
  63. H. Nicolai and K. Peeters, “Loop and spin foam quantum gravity: a brief guide for beginners,” in Approaches to Fundamental Physics, edited by I. Stamatescu and E. Seiler (Springer, 2007), pp. 151\bibrangedash 184. arXiv:hep-th/0601129. doi:10.1007/978-3-540-71117-9_9.
  64. T. Thiemann, “The Phoenix project: master constraint programme for loop quantum gravity,” Class. Quantum Grav. 23, 2211 (2006). arXiv:gr-qc/0305080. doi:10.1088/0264-9381/23/7/002.
  65. K. Giesel and T. Thiemann, “Algebraic quantum gravity (AQG): I. Conceptual setup,” Class. Quantum Grav. 24, 2465 (2007). arXiv:gr-qc/0607099. doi:10.1088/0264-9381/24/10/003.
  66. A. Perez, “Black holes in loop quantum gravity,” Rep. Prog. Phys. 80, 126901 (2017). arXiv:1703.09149. doi:10.1088/1361-6633/aa7e14.
  67. R. P. Kerr, “Gravitational field of a spinning mass as an example of algebraically special metrics,” Phys. Rev. Lett. 11, 237 (1963). doi:10.1103/PhysRevLett.11.237.
  68. E. . T. Newman et al., “Metric of a rotating, charged mass,” J. Math. Phys. 6, 918 (1965). doi:10.1063/1.1704351.
  69. S. W. Hawking, “Gravitational radiation from colliding black holes,” Phys. Rev. Lett. 26, 1344 (1971). doi:10.1103/PhysRevLett.26.1344.
  70. D. Christodoulou, “Reversible and irreversible transformations in black-hole physics,” Phys. Rev. Lett. 25, 1596 (1970). doi:10.1103/PhysRevLett.25.1596.
  71. D. Christodoulou and R. Ruffini, “Reversible transformations of a charged black hole,” Phys. Rev. D 4, 3552 (1971). doi:10.1103/PhysRevD.4.3552.
  72. J. M. Bardeen, B. Carter and S. W. Hawking, “The four laws of black hole mechanics,” Commun. Math. Phys. 31, 161 (1973). doi:10.1007/BF01645742.
  73. S. W. Hawking, “Black hole explosions?,” Nature 248, 30 (1974). doi:10.1038/248030a0.
  74. M. Planck, “Zur Theorie des Gesetzes der Energieverteilung im Normalspectrum,” Verh. Dtsch. Phys. Ges. 2, 237 (1900).
  75. A. Einstein, “Über einen die Erzeugung und Verwandlung des Lichtes betreffenden heuristischen Gesichtspunkt,” Ann. Phys. (Leipzig) 17, 132 (1905). doi:10.1002/andp.19053220607.
  76. W. G. Unruh, “Notes on black-hole evaporation,” Phys. Rev. D 14, 870 (1976). doi:10.1103/PhysRevD.14.870.
  77. A. Ashtekar, J. C. Baez and K. Krasnov, “Quantum geometry of isolated horizons and black hole entropy,” Adv. Theor. Math. Phys. 4, 1 (2000). arXiv:gr-qc/0005126. doi:10.4310/ATMP.2000.v4.n1.a1.
  78. M. Domagala and J. Lewandowski, “Black-hole entropy from quantum geometry,” Class. Quantum Grav. 21, 5233 (2004). arXiv:gr-qc/0407051. doi:10.1088/0264-9381/21/22/014.
  79. K. A. Meissner, “Black-hole entropy in loop quantum gravity,” Class. Quantum Grav. 21, 5245 (2004). arXiv:gr-qc/0407052. doi:10.1088/0264-9381/21/22/015.
  80. A. Ghosh and P. Mitra, “An improved estimate of black hole entropy in the quantum geometry approach,” Phys. Lett. B 616, 114 (2005). arXiv:gr-qc/0411035. doi:10.1016/j.physletb.2005.05.003.
  81. J. Engle, K. Noui and A. Perez, “Black hole entropy and SU(2) Chern-Simons theory,” Phys. Rev. Lett. 105, 031302 (2010). arXiv:0905.3168. doi:10.1103/PhysRevLett.105.031302.
  82. R. K. Kaul and P. Majumdar, “Logarithmic correction to the Bekenstein-Hawking entropy,” Phys. Rev. Lett. 84, 5255 (2000). arXiv:gr-qc/0002040. doi:10.1103/PhysRevLett.84.5255.
  83. A. Ghosh and A. Perez, “Black hole entropy and isolated horizons thermodynamics,” Phys. Rev. Lett. 107, 241301 (2011). arXiv:1107.1320. doi:10.1103/PhysRevLett.107.241301.
  84. E. Bianchi, “Entropy of non-extremal black holes from loop gravity” (2012). arXiv:1204.5122.
  85. A. Ghosh, K. Noui and A. Perez, “Statistics, holography, and black hole entropy in loop quantum gravity,” Phys. Rev. D 89, 084069 (2014). arXiv:1309.4563. doi:10.1103/PhysRevD.89.084069.
  86. R. P. Feynman, “Space-time approach to non-relativistic quantum mechanics,” Rev. Mod. Phys. 20, 367 (1948). doi:10.1103/RevModPhys.20.367.
  87. G. Ponzano and T. Regge, “Semiclassical limit of Racah coefficients,” in Spectroscopic and Group Theoretical Methods in Physics, edited by F. Bloch, S. . G. Cohen, S. Sambursky and I. Talmi (North-Holland, 1968), pp. 1\bibrangedash 58.
  88. V. G. Turaev and O. Y. Viro, “State sum invariants of 3-manifolds and quantum 6j6j-symbols,” Topology 31, 865 (1992). doi:10.1016/0040-9383(92)90015-A.
  89. H. Ooguri, “Topological lattice models in four dimensions,” Mod. Phys. Lett. A 7, 2799 (1992). arXiv:hep-th/9205090. doi:10.1142/S0217732392004171.
  90. L. Crane and D. Yetter, “A categorical construction of 4D topological quantum field theories,” in Quantum Topology, edited by L. H. Kauffman and R. A. Baadhio (World Scientific, 1993), pp. 120\bibrangedash 130. arXiv:hep-th/9301062. doi:10.1142/9789812796387_0005.
  91. J. W. Barrett and L. Crane, “Relativistic spin networks and quantum gravity,” J. Math. Phys. 39, 3296 (1998). arXiv:gr-qc/9709028. doi:10.1063/1.532254.
  92. W. Kamiński, M. Kisielowski and J. Lewandowski, “Spin-foams for all loop quantum gravity,” Class. Quantum Grav. 27, 095006 (2010). arXiv:0909.0939. doi:10.1088/0264-9381/27/9/095006.
  93. L. Freidel, “Group field theory: an overview,” Int. J. Theor. Phys. 44, 1769 (2005). arXiv:hep-th/0505016. doi:10.1007/s10773-005-8894-1.
  94. T. Regge, “General relativity without coordinates,” Nuovo Cimento 19, 558 (1961). doi:10.1007/BF02733251.
  95. J. Roberts, “Classical 6j6j-symbols and the tetrahedron,” Geom. Topol. 3, 21 (1999). arXiv:math-ph/9812013. doi:10.2140/gt.1999.3.21.
  96. K. Noui and A. Perez, “Three-dimensional loop quantum gravity: physical scalar product and spin-foam models,” Class. Quantum Grav. 22, 1739 (2005). arXiv:gr-qc/0402110. doi:10.1088/0264-9381/22/9/017.
  97. J. F. Plebański, “On the separation of Einsteinian substructures,” J. Math. Phys. 18, 2511 (1977). doi:10.1063/1.523215.
  98. J. Engle and R. Pereira, “Regularization and finiteness of the Lorentzian loop quantum gravity vertices,” Phys. Rev. D 79, 084034 (2009). arXiv:0805.4696. doi:10.1103/PhysRevD.79.084034.
  99. J. W. Barrett et al., “Asymptotic analysis of the Engle-Pereira-Rovelli-Livine four-simplex amplitude,” J. Math. Phys. 50, 112504 (2009). arXiv:0902.1170. doi:10.1063/1.3244218.
  100. J. W. Barrett et al., “Lorentzian spin foam amplitudes: graphical calculus and asymptotics,” Class. Quantum Grav. 27, 165009 (2010). arXiv:0907.2440. doi:10.1088/0264-9381/27/16/165009.
  101. A. Ashtekar and P. Singh, “Loop quantum cosmology: a status report,” Class. Quantum Grav. 28, 213001 (2011). arXiv:1108.0893. doi:10.1088/0264-9381/28/21/213001.