Background independent quantum gravity: A status report

Classical and Quantum Gravity

Volumn 21, Issue 15, 2004, Pages

  Ashtekar, Abhay ^a,b,c   Lewandowski, Jerzy ^a,b,c,d  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

^b ALBERT EINSTEIN INSTITUT   (Germany)

^c Erwin Schrodinger International Institute for Mathematical Physics   (Austria)

^d UNIVERSITY OF WARSAW   (Poland)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 4043142118     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/21/15/R01     Document Type: Review

References (233)

1. Creutz M 1983 Quarks, Gluons and Lattices (Cambridge: Cambridge University Press)
2. Ashtekar A 1991 Lectures on Non-Perturbative Canonical Gravity (Singapore: World Scientific) notes prepared in collaboration with R S Tate
3. Baez J and Muniain J P 1994 Gauge Fields, Knots and Gravity (Singapore: World Scientific)
4. Gambini R and Pullin J 1996 Loops, Knots, Gauge Theories and Quantum Gravity (Cambridge: Cambridge University Press)
5. Carlip S 1998 Quantum Gravity in 2 + 1 Dimensions (Cambridge: Cambridge University Press)
6. Rovelli C 1998 Loop quantum gravity Liv. Rev, Rel 11
7. Bojowald M 2001 Quantum Geometry and Symmetry (Aachen: Saker-Verlag)
8. Ashtekar A 2002 Quantum geometry and gravity: recent advances General Relativity and Gravitation ed N T Bishop and S D Maharaj (Singapore: World Scientific) (Preprint gr-qc/0112038)
9. Thiemann T 2002 Lectures on loop quantum gravity Preprint gr-qc/0210094 (2003 Aspects of Quantum Gravity: From Theory to Experimental Search (Lecture Notes in Physics) (Berlin: Springer) at press) Thiemann T 2001 Preprint gr-qc/0110034 (2004 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press) at press)
10. Thiemann T 2002 Lectures on loop quantum gravity Preprint gr-qc/0210094 (2003 Aspects of Quantum Gravity: From Theory to Experimental Search (Lecture Notes in Physics) (Berlin: Springer) at press) Thiemann T 2001 Preprint gr-qc/0110034 (2004 Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press) at press)
11. Perez A 2003 Spin foam models for quantum gravity Class. Quantum Grav. 20 R43-104
12. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press) at press Classical theory
13. Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244-7
14. Ashtekar A 1987 New Hamiltonian formulation of general relativity Phys. Rev. D 36 1587-602
15. Samuel J 1987 A Lagrangian basis for Ashtekar's reformulation of canonical gravity Pramana J. Phys. 28 L429-32 Jacobson T and Smolin L 1987 The left handed spin connection as a variable for canonical gravity Phys. Lett. B 196 39-42
16. Samuel J 1987 A Lagrangian basis for Ashtekar's reformulation of canonical gravity Pramana J. Phys. 28 L429-32 Jacobson T and Smolin L 1987 The left handed spin connection as a variable for canonical gravity Phys. Lett. B 196 39-42
17. Ashtekar A, Mazur P and Torre C G 1987 ERST structure of general relativity in terms of new variables Phys. Rev. D 36 2955-62
18. Ashtekar A, Romano J D and Tate R S 1989 New variables for gravity: inclusion of matter Phys. Rev. D 40 2572-87
19. Jacobson T 1988 New variables for canonical supergravity Class. Quantum Grav. 5 923-35 Matschull H J and Nicolai H 1994 Canonical quantum supergravity in three-dimensions Nucl. Phys. B 411 609-46
20. Jacobson T 1988 New variables for canonical supergravity Class. Quantum Grav. 5 923-35 Matschull H J and Nicolai H 1994 Canonical quantum supergravity in three-dimensions Nucl. Phys. B 411 609-46
21. Ashtekar A, Balachandran A P and Jo S 1989 The CP problem in quantum gravity Int. J. Mod. Phys. A 4 1493-514
22. Plebański J F 1977 On the separation of Einsteinian substructures J. Math. Phys. 18 2511
23. Capovilla R, Dell J and Jacobson T 1989 General relativity without a metric Phys. Rev. Lett. 63 2325-8 Capovilla R, Dell J, Jacobson T and Mason L 1991 Selfdual two forms and gravity Class. Quantum Grav. 8 41-57
24. Capovilla R, Dell J and Jacobson T 1989 General relativity without a metric Phys. Rev. Lett. 63 2325-8 Capovilla R, Dell J, Jacobson T and Mason L 1991 Selfdual two forms and gravity Class. Quantum Grav. 8 41-57
25. Holst S 1996 Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action Phys. Rev. D 53 5966-9 Wisniewski J 2001 Symplectic structure from Holst action Preprint
26. Holst S 1996 Barbero's Hamiltonian derived from a generalized Hilbert-Palatini action Phys. Rev. D 53 5966-9 Wisniewski J 2001 Symplectic structure from Holst action Preprint
27. Samuel J 2000 Is Barbero's Hamiltonian formulation a gauge theory of Lorentzian gravity? Class. Quantum Grav. 17 L141-8
28. Robinson D C1995 A Lagrangian formalism for the Einstein-Yang-Mills equations J, Math. Phys. 36 3733-42
29. Lewandowski J and Okol'ow A 2000 2-form gravity of the Lorentzian signature Class. Quantum Grav. 17 L47-51
30. Alexandrov S and Livine E R 2003 SU/(2) loop quantum gravity seen from covariant theory Phys. Rev. D 67 044009
31. Freidel L and Krasnov K 1999 BF description of higher dimensional gravity theories Adv. Theor. Math. Phys. 31289-324
32. Jacobson T and Romano J D 1992 Degenerate extensions of general relativity Class. Quantum Grav. 9 L119-24
33. Matschull H J 1996 Causal structure and diffeomorphisms in Ashtekar's gravity Class. Quantum Grav. 13 765-82
34. Jacobson T 1996 (1 + 1) sector of (3 +1) gravity Class. Quantum Grav. 13 L111-6 Jacobson T 1996 Class. Quantum Grav. 13 3269 (erratum)
35. Jacobson T 1996 (1 + 1) sector of (3 +1) gravity Class. Quantum Grav. 13 LI 11-6 Jacobson T 1996 Class. Quantum Grav. 13 3269 (erratum)
36. Lewandowski J and Wisniewski J 1997 (2 + 1) sector of (3 +1) gravity Class. Quantum Grav. 14 775-82
37. Lewandowski J and Wisniewski J 1999 Degenerate sectors of the Ashtekar gravity Class. Quantum Grav. 16 3057-69
38. Penrose R 1976 Non-linear graviton and curved twistor theory Gen. Rel. Grav. 731-52
39. Ko M, Ludvigsen M, Newman E T and Tod P 1981 The theory of W space Phys. Rep. 71 51-139 Connections and loops
40. Rovelli C and Smolin L 1988 Knot theory and quantum gravity Phys. Rev. Lett. 61 1155-8
41. Rovelli C and Smolin L 1990 Loop representation for quantum general relativity Nucl. Phys. B 331 80-152
42. Ashtekar A, Husain V, Rovelli C, Samuel J and Smolin L 1989 2+1 quantum gravity as a toy model for the 3+1 theory Class. Quantum Grav. 6 L185-93
43. Ashtekar A, Rovelli C and Smolin L 1991 Gravitons and loops Phys. Rev. D 44 1740-55
44. Smolin L 1992 Recent developments in non-perturbative quantum gravity Quantum Gravity and Cosmology ed J Mercader, J Solá and R Verdaguer (Singapore: World Scientific)
45. Goldberg J N, Lewandowski J and Stomaiolo C 1992 Degeneracy in loop variables Commun. Math. Phys. 148 377-402 Background-independent quantization of theories of connections
46. Ashtekar A and Isham C J 1992 Representation of the holonomy algebras of gravity and non-Abelian gauge theories Class. Quantum Grav. 9 1433-67
47. Ashtekar A and Lewandowski J 1994 Representation theory of analytic holonomy algebras Knots and Quantum Gravity ed J C Baez (Oxford: Oxford University Press)
48. Baez J C 1994 Generalized measures in gauge theory Lett. Math. Phys. 31 213-23
49. Lewandowski J 1994 Topological measure and graph-differential geometry on the quotient space of connections Int. J. Mod. Phys. D 3 207-10
50. Ashtekar A, Lewandowski L, Marolf D, Mourão J and Thiemann T 1995 A manifestly gauge invariant approach to quantum gauge theories Geometry of Constrained Dynamical Systems ed J M Charap (Cambridge: Cambridge University Press) pp 60-72
51. Marolf D and Mourão J 1995 On the support of the Ashtekar-Lewandowski measure Commun. Math. Phys. 170 583-606
52. Asntekar A and Lewandowski J 1995 Projective techniques and functional integration J. Math. Phys. 36 2170-91
53. Ashtekar A, Lewandowski L, Marolf D, Mourão J and Thiemann T 1996 Coherent state transforms for spaces of connections J. Funct. Anal. 135 519-51
54. Baez J C and Sawin S 1997 Functional integration on spaces of connections J. Funct. Anal. 150 1-27
55. Ashtekar A, Corichi A and Zapata JA 1998 Quantum theory of geometry: III. Non-commutativity of Riemannian structures Class. Quantum Grav. 15 2955-72
56. Marolf D. Mourão J and Thiemann T 1997 The status of diffeomorpnism superselection in Euclidean 2 + 1 gravity J. Math. Phys. 38 4730-40
57. Mourão J M, Thiemann T and Velhinho J M 1999 Physical properties of quantum field theory measures J. Math. Phys. 40 2337-53
58. Velhinho J M 2002 A groupoid approach to spaces of generalized connections J. Geom. Phys. 41 166-80
59. Fleischhack C 2000 Stratification of the generalized gauge orbit space Commun. Math. Phys. 214 607-49
60. Fleischhack C 2003 On the Gribov problem for generalized connections Commun. Math. Phys. 234 423-54
61. Fleischhack C 2003 Hyphs and the Ashtekar-Lewandowski measure J. Geom. Phys. 45 231-51
62. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H 2002 Some comments on the representation theory of the algebra underlying loop quantum gravity Preprint gr-qc/0207111.
63. Sahlmann H 2002 When do measures on the space of connections support the triad operators of loop quantum gravity? Preprint gr-qc/0207112 Sahlmann H 2002 Some comments on the representation theory of the algebra underlying loop quantum gravity Preprint gr-qc/0207111.
64. Okolów A and Lewandowski J 2003 Diffeomoiphism covariant representations of the holonomy-flux star-algebra Class. Quantum Grav. 20 3543-68
65. Sahlmann H and Thiemann T 2003 On the superseleotion theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Sahlmann H and Thiemann T 2003 Irreducibility of the Ashtekar-Isham-Lewandowski representation Preprint gr-qc/0303074
66. Sahlmann H and Thiemann T 2003 On the superseleotion theory of the Weyl algebra for diffeomorphism invariant quantum gauge theories Preprint gr-qc/0302090 Sahlmann H and Thiemann T 2003 Irreducibility of the Ashtekar-Isham-Lewandowski representation Preprint gr-qc/0303074
67. Lewandowski J, Okolów A, Sahlmann H and Thiemann T 2003 Uniqueness of the diffeomorphism invariant state on the quantum holonomy-flux algebra Preprint Spin networks
68. Penrose R 1971 Angular momentum: an approach to combinatorial space-time Quantum Theory and Beyond ed T Bastin (Cambridge: Cambridge University Press)
69. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 52 5743-59
70. Baez J C 1996 Spin networks in non-perturbative quantum gravity The Interface of Knots and Physics ed L Kauffman (Providence, RI: American Mathematical Society) pp 167-203 Baez J C 1996 Spin networks in gauge theory Adv. Math. 117 253-72
71. Baez J C 1996 Spin networks in non-perturbative quantum gravity The Interface of Knots and Physics ed L Kauffman (Providence, RI: American Mathematical Society) pp 167-203 Baez J C 1996 Spin networks in gauge theory Adv. Math. 117 253-72
72. Thiemann T 1998 The inverse loop transform J. Math. Phys. 39 1236-48
73. Baez J C and Sawin S 1998 Diffeomorphism-invariant spin network states J. Funct. Anal. 158 253-66
74. Fleischhack C 2003 Proof of a conjecture by Lewandowski and Thiemann Preprint math-ph/0304002 Geometric operators and their properties
75. Rovelli C and Smolin L 1995 Discreteness of area and volume in quantum gravity Nucl. Phys. B 442 593-622 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 753 (erratum)
76. Rovelli C and Smolin L 1995 Discreteness of area and volume in quantum gravity Nucl. Phys. B 442 593-622 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 753 (erratum)
77. Ashtekar A and Lewandowski L 1995 Differential geometry on the space of connections using projective techniques J. Geom. Phys. 17 191-230
78. Loll R 1995 The volume operator in discretized quantum gravity Phys. Rev. Lett. 75 3048-51
79. Loll R 1995 Spectrum of the volume operator in quantum gravity Nucl. Phys. B 460 143-54
80. Frittelli S, Lehner L and Rovelli C 1996 Class. Quantum Grav. 13 2921-32
81. De Pietri R and Rovelli C 1996 Phys. Rev. D 54 2664-90
82. Lewandowski J 1997 Volume and quantizations Class. Quantum Grav. 14 71-6
83. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry: I. Area operators Class. Quantum Grav. 14 A55-81
84. Ashtekar A and Lewandowski J 1997 Quantum theory of geometry: H Volume operators Adv. Theor. Math. Phys. 1388-429
85. Loll R 1997 Simplifying the spectral analysis of the volume operator Nucl. Phys. B 500 405-20
86. Loll R 1997 Further results on geometric operators in quantum gravity Class. Quantum Grav. 14 1725-41
87. De Pietri R 1997 Spin networks and recoupling in loop quantum gravity Nucl. Phys. Suppl. 57 251-4
88. De Pietri R 1997 On the relation between the connection and the loop representation of quantum gravity Class. Quantum Grav. 14 53-70
89. Thiemann T 1998 Closed formula for the matrix elements of the volume operator in canonical quantum gravity J. Math. Phys. 39 3347-71
90. Thiemann T 1998 A length operator for canonical quantum gravity J. Math. Phys. 39 3372-92
91. Major S A 1999 Operators for quantized directions Class. Quantum Grav. 16 3859-77 Barbero-Immirzi ambiguity
92. Barbero F 1996 Real Ashtekar variables for Lorentzian signature spacetimes Phys. Rev. D 51 5507-10
93. Immirzi G 1997 Quantum gravity and Regge calculus Nucl. Phys. Proc. Suppl. 57 65-72
94. Rovelli C and Thiemann T 1998 The Immirizi parameter in quantum general relativity Phys. Rev. D 57 1009-14
95. Gambini R, Obregon O and Pullin J 1999 Yang-Mills analogues of the Immirzi ambiguity Phys. Rev. D 59 047505 Quantum Einstein's equation I
96. Kuchař K 1993 Canonical quantum gravity General Relativity and Gravitation 1992 ed R J Gleiser, C N Kozameh and O M Moreschi (Bristol: Institute of Physics Publishing) pp 119-50
97. Ashtekar A, Tate R S and Uggla C1993 Minisuperspaces: observables and quantization Int. J. Phys. D 2 15-50 Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: symmetries and quantization Misner Festschrift ed B L Hu et al (Cambridge: Cambridge University Press)
98. Ashtekar A, Tate R S and Uggla C1993 Minisuperspaces: observables and quantization Int. J. Phys. D 2 15-50 Ashtekar A, Tate R S and Uggla C 1993 Minisuperspaces: symmetries and quantization Misner Festschrift ed B L Hu et al (Cambridge: Cambridge University Press)
99. Ashtekar A and Tate R S 1994 An algebraic extension of Dirac quantization: examples J. Math. Phys. 35 6434-70
100. Marolf D 1995 Refined algebraic quantization: systems with a single constraint Preprint gr-qc/9508015
101. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456-93
102. Marolf D, Mourão J and Thiemann T 1997 The status of diffeomorphism super-selection in Euclidean 2 +1 gravity J. Math. Phys. 38 4730-40
103. Guilini N and Marolf D 1999 On the generality of refined algebraic quantization Class. Quantum Grav. 16 2479-88 Guilini N and Marolf D 1999 A uniqueness theorem for constraint quantization Class. Quantum Grav. 16 2489-505
104. Guilini N and Marolf D 1999 On the generality of refined algebraic quantization Class. Quantum Grav. 16 2479-88 Guilini N and Marolf D 1999 A uniqueness theorem for constraint quantization Class. Quantum Grav. 16 2489-505
105. Lewandowski J and Thiemann T 1999 Diffeomorphism invariant quantum field theories of connections in terms of webs Class. Quantum Grav. 16 2299-322
106. Corichi A and Zapata J A 1997 On diffeomorphism invariance for lattice theories Nucl. Phys. B 493 475-90 Quantum Einstein's equation II
107. Rovelli C and Smolin L 1994 The physical Hamiltonian in nonperturbative quantum gravity Phys. Rev. Lett. 72 446-9
108. Thiemann T 1996 Anomaly-free formulation of non-perturbative, four-dimensional Lorentzian quantum gravity Phys. Lett. B 380 257-64
109. Thiemann T 1998 Quantum spin dynamics (QSD) Class. Quantum Grav. 15 839-73
110. Thiemann T 1998 QSD: III. Quantum constraint algebra and physical scalar product in quantum general relativity Class. Quantum Grav. 15 1207-47
111. Thiemann T 1998 QSD: V. Quantum gravity as the natural regulator of matter quantum field theories Class. Quantum Grav. 15 1281-314
112. Thiemann T 2001 Quantum spin dynamics (QSD): VII. Symplectic structures and continuum lattice formulations of gauge field theories Class. Quantum Grav. 18 3293-338
113. Gambini R, Lewandowski J, Marolf D and Pullin J 1998 On the consistency of the constraint algebra in spin network quantum gravity Int. J. Mod. Phys. D 7 97-109
114. Lewandowski J and Marolf D 1998 Loop constraints: a habitat and their algebra Int. J. Mod. Phys. D 7 299-330
115. Gaul G and Rovelli C 2001 Generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements Class. Quantum Grav. 18 1593-624 Big-bang
116. Kodama H 1988 Specialization of Ashtekar's formalism to Bianchi cosmology Prog. Theor. Phys. 80 1024-40 Kodama H 1990 Holomorphic wavefunction of the universe Phys. Rev. D 42 2548-65
117. Kodama H 1988 Specialization of Ashtekar's formalism to Bianchi cosmology Prog. Theor. Phys. 80 1024-40 Kodama H 1990 Holomorphic wavefunction of the universe Phys. Rev. D 42 2548-65
118. Bojowald M 2001 Absence of singularity in loop quantum cosmology Phys. Rev. Lett. 86 5227-30
119. Bojowald M 2001 Inverse scale factor in isotropic quantum geometry Phys. Rev. D 64 084018
120. Bojowald M 2001 Dynamical initial conditions in quantum cosmology Phys. Rev. Lett. 87 121301
121. Bojowald M 2001 Loop quantum cosmology: IV. Discrete time evolution Class. Quantum Grav. 18 1071-88
122. Bojowald M 2001 Loop quantum cosmology: III. Wheeler-DeWitt operators Class. Quantum Grav. 18 1055-70 Bojowald M 2002 The semiclassical limit of loop quantum cosmology Class. Quantum Grav. 18 L109-16
123. Bojowald M 2001 Loop quantum cosmology: III. Wheeler-DeWitt operators Class. Quantum Grav. 18 1055-70 Bojowald M 2002 The semiclassical limit of loop quantum cosmology Class. Quantum Grav. 18 L109-16
124. Bojowald M 2001 The inverse scale factor in isotropic quantum geometry Phys. Rev. D 64 084018
125. Bojowald M 2002 Isotropic loop quantum cosmology Class. Quantum Grav. 19 2717-42
126. Bojowald M and Hinterleitner F 2002 Isotropic loop quantum cosmology with matter Phys. Rev. D 66 104003
127. Bojowald M and Vandersloot K 2003 Loop quantum cosmology, boundary proposals, and inflation Phys. Rev. D 67 124023
128. Bojowald M 2003 Homogeneous loop quantum cosmology Class. Quantum Grav. 20 2595-615
129. Bojowald M 2003 Gen. Rel. Grav. 35 1877-83 first prize in the Gravity Research Foundation Essay Contest (Initial conditions for a universe Preprint gr-qc/0305069)
130. Ashtekar A, Bojowald M and Lewandowski J 2003 Mathematical structure of loop quantum cosmology Adv. Theor. Math. Phys. 7 233-68
131. Bojowald M, Date G and Vandersloot K 2004 Homogeneous loop quantum cosmology: the role of the spin connection Class. Quantum Grav. 21 1253-78
132. Ashtekar A, Bojowald M and Willis J 2004 Quantum corrections to Friedmann equations in loop quantum cosmology (in preparation) Black holes
133. Bekenstein J D 1973 Black holes and entropy Phys. Rev. D 7 2333-46 Bekenstein J D 1974 Generalized second law of thermodynamics in black hole physics Phys. Rev. D 9 3292-300
134. Bekenstein J D 1973 Black holes and entropy Phys. Rev. D 7 2333-46 Bekenstein J D 1974 Generalized second law of thermodynamics in black hole physics Phys. Rev. D 9 3292-300
135. Bekenstein J D and Meisels A 1977 Einstein A and B coefficients for a black hole Phys. Rev. D 15 2775-81
136. Bardeen J W, Carter B and Hawking S W 1973 The four laws of black hole mechanics Commun. Math. Phys. 31161-70
137. Hawking S W 1975 Particle creation by black holes Commun. Math. Phys. 43 199-220
138. Gibbons G and Hawking S W 1977 Cosmological event horizons, thermodynamics, and particle creation Phys. Rev. D 15 2738-51
139. Smolin L 1995 Linking topological quantum field theory and nonperturbative quantum gravity J. Math. Phys. 36 6417-55
140. Barreira M, Carfora M and Rovelli C 1996 Physics with non-perturbative quantum gravity: radiation from a quantum black hole Gen. Rel. Grav. 28 1293-9 Rovelli C 1996 Black hole entropy from loop quantum gravity Phys. Rev. Lett. 14 3288-91 Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta. 69 582-611
141. Barreira M, Carfora M and Rovelli C 1996 Physics with non-perturbative quantum gravity: radiation from a quantum black hole Gen. Rel. Grav. 28 1293-9 Rovelli C 1996 Black hole entropy from loop quantum gravity Phys. Rev. Lett. 14 3288-91 Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta. 69 582-611
142. Barreira M, Carfora M and Rovelli C 1996 Physics with non-perturbative quantum gravity: radiation from a quantum black hole Gen. Rel. Grav. 28 1293-9 Rovelli C 1996 Black hole entropy from loop quantum gravity Phys. Rev. Lett. 14 3288-91 Rovelli C 1996 Loop quantum gravity and black hole physics Helv. Phys. Acta. 69 582-611
143. Krasnov K 1997 Geometrical entropy from loop quantum gravity Phys. Rev. D 55 3505-13 Krasnov K 1998 On statistical mechanics of Schwarzschild black holes Gen. Rel. Grav. 30 53-68
144. Krasnov K 1997 Geometrical entropy from loop quantum gravity Phys. Rev. D 55 3505-13 Krasnov K 1998 On statistical mechanics of Schwarzschild black holes Gen. Rel. Grav. 30 53-68
145. Jacobson T, Kang G and Myers R C 1994 On black hole entropy Phys. Rev. D 49 6587-98
146. Wald R 1993 Black hole entropy is Noether charge Phys. Rev. D 48 3427-31 Iyer V and Wald R 1994 Some properties of Noether charge and a proposal for dynamical black hole entropy Phys. Rev. D 50 846-64
147. Wald R 1993 Black hole entropy is Noether charge Phys. Rev. D 48 3427-31 Iyer V and Wald R 1994 Some properties of Noether charge and a proposal for dynamical black hole entropy Phys. Rev. D 50 846-64
148. Ashtekar A, Baez I C, Corichi A and Krasnov K 1998 Quantum geometry and black hole entropy Phys. Rev. Lett. 80 904-7
149. Ashtekar A, Corichi A and Krasnov K 1999 Isolated horizons: the classical phase space Adv. Theor. Math. Phys. 3 418-71
150. Ashtekar A, Baez J C and Krasnov K 2000 Quantum geometry of isolated horizons and black hole entropy Adv. Theor. Math. Phys. 4 1-95
151. Kaul R K and Majumdar P 2000 Logarithmic corrections to the Bekenstein-Hawking entropy Phys. Rev. Lett. 84 5255-7
152. Ashtekar A, Beetle C and Fairhurst S 1999 Isolated horizons: a generalization of black hole mechanics Class. Quantum Grav. 16 L1-7 Ashtekar A, Beetle C and Fairhurst S 2000 Mechanics of isolated horizons Class. Quantum Grav. 17 253-98
153. Ashtekar A, Beetle C and Fairhurst S 1999 Isolated horizons: a generalization of black hole mechanics Class. Quantum Grav. 16 L1-7 Ashtekar A, Beetle C and Fairhurst S 2000 Mechanics of isolated horizons Class. Quantum Grav. 17 253-98
154. Lewandowski J 2000 Spacetimes admitting isolated horizons Class. Quantum Grav. 17 L53-9
155. Ashtekar A, Fairhurst S and Krishnan B 2000 Isolated horizons; Hamiltonian evolution and the first law Phys. Rev. D 62 104025
156. Ashtekar A, Beetle C and Lewandowski J 2001 Mechanics of rotating isolated horizons Phys. Rev. D 64 044016
157. Ashtekar A, Beetle C and Lewandowski J 2002 Geometry of generic isolated horizons Class. Quantum Grav. 19 1195-225
158. Ashtekar A, Corichi A and Sudarski D 2003 Non-minimally coupled scalar fields and isolated horizons Class. Quantum Grav. 20 3413-25
159. Ashtekar A and Corichi A 2003 Non-minimal couplings, quantum geometry and black hole entropy Class. Quantum Grav. 20 4473-84
160. Ashtekar A, Engle J, Pawlowski T and van der Broeck C 2004 Multipole moments of isolated horizons Class. Quantum Grav. 21 2549-70
161. Ashtekar A 2003 Black hole entropy: inclusion of distortion and angular momentum, online at http://www.phys.psu.edu/events/index.html?event_id= 517&event-type=17 Ashtekar A, Engle J and van der Broeck C 2004 in preparation
162. Ashtekar A 2003 Black hole entropy: inclusion of distortion and angular momentum, online at http://www.phys.psu.edu/events/index.html?event_id= 517&event-type=17 Ashtekar A, Engle J and van der Broeck C 2004 in preparation
163. Wheeler J A 1992 It from bit Sakharov Memorial Lectures on Physics vol 2, ed L Keldysh and V Feinberg (Moscow: Nova Science)
164. Ghosh A and Mitra P 2004 A bound on the log correction to the black hole area law Preprint gr-qc/0401070 Low energy physics:
165. Ashtekar A, Rovelli C and Smolin L 1992 Weaving a classical geometry with quantum threads Phys. Rev. Lett. 69 237-40
166. Arnsdorf M and Gupta S 2000 Loop quantum gravity on non-compact spaces Nucl. Phys. B 577 529-46
167. Corichi A and Reyes J M 2001 A Gaussian weave for kinematical loop quantum gravity Int. J. Mod. Phys. D 10 325-38
168. Hall B C 1994 The Segal-Bergmann coherent state transform for compact Lie groups J. Fund. Anal. 122 103-51
169. Sahlmann H, Thiemann T and Winkler O 2001 Coherent states for canonical quantum general relativity and the infinite tensor product extension Nucl. Phys. B 606 401-40
170. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025-64 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-82 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit Class. Quantum Grav. 18 4997-5054
171. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025-64 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-82 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit Class. Quantum Grav. 18 4997-5054
172. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025-64 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-82 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit Class. Quantum Grav. 18 4997-5054
173. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025-64 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): II. Peakedness properties Class. Quantum Grav. 18 2561-636 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): III. Ehrenfest theorems Class. Quantum Grav. 18 4629-82 Thiemann T and Winkler O 2001 Gauge field theory coherent states (GCS): IV. Infinite tensor product and thermodynamical limit Class. Quantum Grav. 18 4997-5054
174. Sahlmann H and Thiemann T 2002 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Preprint gr-qc/0207030 Sahlmann H and Thiemann T 2002 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Preprint gr-qc/0207031
175. Sahlmann H and Thiemann T 2002 Towards the QFT on curved spacetime limit of QGR: I. A general scheme Preprint gr-qc/0207030 Sahlmann H and Thiemann T 2002 Towards the QFT on curved spacetime limit of QGR: II. A concrete implementation Preprint gr-qc/0207031
176. Thiemann T 2002 Complexifier coherent states for quantum general relativity Preprint gr-qc/0206037
177. Bombelli L 2002 Statistical geometry of random weave states Proc. 9th Marcel Grossmann Meeting on General Relativity ed V G Gurzadyan, R T Jantzen and R Ruffini (Singapore: World Scientific) (Preprint gr-qc/0101080)
178. Ashtekar A and Isham C J 1992 Phys. Lett. B 274 393-8
179. Varadarajan M 2000 Fock representations from U(1) holonomy algebras Phys. Rev. D 61 104001 Varadarajan M 2001 Photons from quantized electric flux representations Phys. Rev. D 64 104003
180. Varadarajan M 2000 Fock representations from U(1) holonomy algebras Phys. Rev. D 61 104001 Varadarajan M 2001 Photons from quantized electric flux representations Phys. Rev. D 64 104003
181. Ashtekar A and Lewandowski J 2001 Relation between polymer and Fock excitations Class. Quantum Grav. 18 L117-27
182. Velhinho J M 2002 Invariance properties of induced Fock measures for U(1) holonomies Commun. Math. Phys. 227 541-50
183. Ashtekar A, Fairhurst S and Willis J 2003 Quantum gravity, shadow states, and quantum mechanics Class. Quantum Grav. 20 1031-61
184. Ashtekar A, Fairhurst S and Ghosh A 2004 (in preparation)
185. Varadarajan M 2002 Gravitons from a loop representation of linearised gravity Phys. Rev. D 66 024017
186. Ashtekar A, Ghosh A and Van Den Broeck C 2004 (in preparation)
187. Bobienski M, Lewandowski J and Mroczek M 2002 A 2-surface quantization of the Lorentzian gravity Proc. 9th Marcel Grossmann Meeting on General Relativity ed V G Gurzadyan, R T Jantzen and R Ruffini (Singapore: World Scientific) (Preprint gr-qc/0101069)
188. Ashtekar A, Lewandowski J and Sahlmann H 2003 Polymer and Fock representations of a scalar field Class. Quantum Grav. 20 L11-21 Spin foams and finiteness
189. Baez J C 2000 An introduction to spin foam models of quantum gravity and BF theory Lect. Notes Phys. 543 25-94
190. Baez J C 1998 Spin foam models Class. Quantum Grav. 15 1827-58
191. Reisenberger M P 1997 A lattice worldsheet sum for 4-d Euclidean general relativity Preprint gr-qc/9711052 Reisenberger M P 1999 On relativistic spin network vertices J. Math. Phys. 40 2046-54
192. Reisenberger M P 1997 A lattice worldsheet sum for 4-d Euclidean general relativity Preprint gr-qc/9711052 Reisenberger M P 1999 On relativistic spin network vertices J. Math. Phys. 40 2046-54
193. Reisenberger M P and Rovelli C 2001 Spacetime as a Feynman diagram: the connection formulation Class. Quantum Grav. 18 221-40 Reisenberger M P and Rovelli 2002 Spacetime states and covariant quantum theory Phys. Rev. D 65 125016
194. Reisenberger M P and Rovelli C 2001 Spacetime as a Feynman diagram: the connection formulation Class. Quantum Grav. 18 221-40 Reisenberger M P and Rovelli 2002 Spacetime states and covariant quantum theory Phys. Rev. D 65 125016
195. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296-302 Barrett J W and Crane L 2000 A Lorentzian signature model for quantum general relativity Class. Quantum Grav. 17 3101-18
196. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296-302 Barrett J W and Crane L 2000 A Lorentzian signature model for quantum general relativity Class. Quantum Grav. 17 3101-18
197. Perez A 2001 Finiteness of a spinfoam model for Euclidean quantum general relativity Nucl. Phys. B 599 427-34 Perez A and Rovelli C 2001 Spin foam model for Lorentzian general relativity Phys. Rev. D 63 041501 Crane L, Perez A and Rovelli C 2001 Perturbative finiteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovelli C 2001 3 + 1 spinfoam model of quantum gravity with spacelike and timelike components Phys. Rev. D 64 064002
198. Perez A 2001 Finiteness of a spinfoam model for Euclidean quantum general relativity Nucl. Phys. B 599 427-34 Perez A and Rovelli C 2001 Spin foam model for Lorentzian general relativity Phys. Rev. D 63 041501 Crane L, Perez A and Rovelli C 2001 Perturbative finiteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovelli C 2001 3 + 1 spinfoam model of quantum gravity with spacelike and timelike components Phys. Rev. D 64 064002
199. Perez A 2001 Finiteness of a spinfoam model for Euclidean quantum general relativity Nucl. Phys. B 599 427-34 Perez A and Rovelli C 2001 Spin foam model for Lorentzian general relativity Phys. Rev. D 63 041501 Crane L, Perez A and Rovelli C 2001 Perturbative finiteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovelli C 2001 3 + 1 spinfoam model of quantum gravity with spacelike and timelike components Phys. Rev. D 64 064002
200. Perez A 2001 Finiteness of a spinfoam model for Euclidean quantum general relativity Nucl. Phys. B 599 427-34 Perez A and Rovelli C 2001 Spin foam model for Lorentzian general relativity Phys. Rev. D 63 041501 Crane L, Perez A and Rovelli C 2001 Perturbative finiteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301 Crane L, Perez A and Rovelli C 2001 3 + 1 spinfoam model of quantum gravity with spacelike and timelike components Phys. Rev. D 64 064002
201. Baez J, Christensen D, Halford T R and Tsang D C 2002 Spin foam models of Riemannian quantum gravity Class. Quantum Grav. 19 4627-48
202. Gambini R and Pullin J 2002 A finite spin-foam-based theory of three and four dimensional quantum gravity Phys. Rev. D 66 024020
203. Lauscher O and Reuter M 2002 Is quantum Einstein gravity non-perturbatively renormalizable? Class. Quantum Grav. 19 483-92
204. Percacci R and Perini D 2003 Asymptotic safety of gravity coupled to matter Phys. Rev. D 68 044018 Perini D 2003 Gravity and matter with asymptotic safety Preprint hep-th/0305053
205. Percacci R and Perini D 2003 Asymptotic safety of gravity coupled to matter Phys. Rev. D 68 044018 Perini D 2003 Gravity and matter with asymptotic safety Preprint hep-th/0305053
206. Bojowald M and Perez A 2003 Spin foam quantization and anomalies Preprint gr-qc/0303026
207. Freidel L and Louapre D 2003 Diffeomorphisms and spin foam models Nucl. Phys. B 662 279-98 Freidel L and Louapre D 2003 Non-perturbative summation over 3D discrete topologies Phys. Rev. D 68 104004 (Preprint hep-th/0211026)
208. Freidel L and Louapre D 2003 Diffeomorphisms and spin foam models Nucl. Phys. B 662 279-98 Freidel L and Louapre D 2003 Non-perturbative summation over 3D discrete topologies Phys. Rev. D 68 104004 (Preprint hep-th/0211026)
209. Perez A and Noui K 2004 Three dimensional loop quantum gravity: coupling to point particles Preprint gr-qc/0402111 Perez A and Noui K 2004 Three dimensional loop quantum gravity: physical scalar product and spin foam models Preprint gr-qc/0402110 Outlook
210. Perez A and Noui K 2004 Three dimensional loop quantum gravity: coupling to point particles Preprint gr-qc/0402111 Perez A and Noui K 2004 Three dimensional loop quantum gravity: physical scalar product and spin foam models Preprint gr-qc/0402110 Outlook
211. Ashtekar A, Lewandowski J, Marolf D, Mourão J and Thiemann T 1997 SU (N) quantum Yang-Mills theory in two dimensions: a complete solution J. Math. Phys. 38 5453-82
212. Ashtekar A and Sahlmann H 2004 (in preparation)
213. Okolw A 2004 Representations of quantum geometry PhD Thesis University of Warsaw
214. Rovelli C and Speziale S 2003 Reconcile Planck-scale discreteness and the Lorentz-Fitzgerald contraction Phys. Rev. D 67 064019
215. Thiemann T 2003 The Phoenix project: master constraint programme for loop quantum gravity Preprint gr-qc/0305080
216. Dittrich B 2004 Testing the master constraint programme for loop quantum gravity, online at http://www.phys.psu.edu/events/index.html?event_id= 850&event.type= 17
217. Klauder J 2003 Affine quantum gravity Int. J. Mod. Phys. D 12 1769-74 Klauder J 2004 The utility of coherent states and other mathematical methods in the foundations of affine quantum gravity Preprint hep-th/0401214
218. Klauder J 2003 Affine quantum gravity Int. J. Mod. Phys. D 12 1769-74 Klauder J 2004 The utility of coherent states and other mathematical methods in the foundations of affine quantum gravity Preprint hep-th/0401214
219. Di Bartolo C, Gambini R, Griego I and Pullin J 2000 Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants Phys. Rev. Lett. 84 2314-7 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure Class. Quantum Orav. 17 3211-38 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra Class. Quantum Grav. 17 3239-64
220. Di Bartolo C, Gambini R, Griego I and Pullin J 2000 Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants Phys. Rev. Lett. 84 2314-7 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure Class. Quantum Orav. 17 3211-38 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra Class. Quantum Grav. 17 3239-64
221. Di Bartolo C, Gambini R, Griego I and Pullin J 2000 Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants Phys. Rev. Lett. 84 2314-7 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: I. Kinematical structure Class. Quantum Orav. 17 3211-38 Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Canonical quantum gravity in the Vassiliev invariants arena: II. Constraints, habitats and consistency of the constraint algebra Class. Quantum Grav. 17 3239-64
222. Gambini R and Pullin J 2003 Canonical quantization of general relativity in discrete spacetimes Phys. Rev. Lett. 90 021301 Gambini R, Porto R and Pullin J 2004 Loss of coherence from discrete quantum gravity Class. Quantum Grav. 21 L51-7 Gambini R, Porto R and Pullin J 2004 A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence Preprint gr-qc/0402118
223. Gambini R and Pullin J 2003 Canonical quantization of general relativity in discrete spacetimes Phys. Rev. Lett. 90 021301 Gambini R, Porto R and Pullin J 2004 Loss of coherence from discrete quantum gravity Class. Quantum Grav. 21 L51-7 Gambini R, Porto R and Pullin 12004 A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism
224. Gambini R and Pullin J 2003 Canonical quantization of general relativity in discrete spacetimes Phys. Rev. Lett. 90 021301 Gambini R, Porto R and Pullin J 2004 Loss of coherence from discrete quantum gravity Class. Quantum Grav. 21 L51-7 Gambini R, Porto R and Pullin J 2004 A relational solution to the problem of time in quantum mechanics and quantum gravity induces a fundamental mechanism for quantum decoherence Preprint gr-qc/0402118
225. Horowitz G T 1998 Quantum states of black holes Black Holes and Relativistic Stars ed R M Wald (Chicago, IL: University of Chicago Press)
226. Carlip S 1999 Entropy from conformal field theory at Killing horizons Class. Quantum Grav. 16 3327-48
227. Dreyer O, Ghosh A and Wisniewski J 2001 Black hole entropy calculations based on symmetries Class. Quantum Grav. 18 1929-38
228. Carlip S 2002 Near-horizon conformal symmetry and black hole entropy Phys. Rev. Lett. 88 241301
229. Ashtekar A and Krishnan B 2002 Dynamical horizons: energy, angular momentum, fluxes and balance laws Phys. Rev. Lett. 89 261101 Ashtekar A and Krishnan B 2003 Dynamical horizons and their properties Phys. Rev. D 68 104030
230. Ashtekar A and Krishnan B 2002 Dynamical horizons: energy, angular momentum, fluxes and balance laws Phys. Rev. Lett. 89 261101 Ashtekar A and Krishnan B 2003 Dynamical horizons and their properties Phys. Rev. D 68 104030
231. Bojowald M 2002 Inflation from quantum geometry Phys. Rev. Lett. 89 261301
232. Bojowald M and Date G 2004 Quantum suppression of the generic chaotic behavior close to cosmological singularities Phys. Rev. Lett. 92 071302
233. Tsujikawa S, Singh P and Maartens R 2003 Loop quantum gravity effects on inflation and the CMB Preprint astro-ph/0311015