Spin foam models for quantum gravity

Classical and Quantum Gravity

Volumn 20, Issue 6, 2003, Pages

  Perez, Alejandro ^a,b  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

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

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0037272589     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/20/6/202     Document Type: Review

References (149)

1. Rovelli C 2000 Notes for a brief history of quantum gravity Preprint gr-qc/0006061
2. Weinberg S 1995 The Quantum Theory of Fields (Cambridge: Cambridge University Press)
3. Ashtekar A and Lewandowski J 2003 Background independent quantum gravity: a status report Preprint to appear
4. Thieman T 2001 Introduction to modern canonical quantum general relativity Preprint gr-qc/0110034
5. Gaul M and Rovelli C 2000 Loop quantum gravity and the meaning of diffeomorphism invariance Lect. Notes Phys. 541 277-324
6. Rovelli C 1998 Loop quantum gravity Living Rev. Gen. Rel. 1
7. Thieman T 1998 Quantum gravity as the natural regulator of matter quantum field theories Class. Quantum Grav. 15 1281-314
8. Thiemann T 2001 Gauge field theory coherent states (GCS): I. General properties Class. Quantum Grav. 18 2025
9. Barrett J W and Crane L 1998 Relativistic spin networks and quantum gravity J. Math. Phys. 39 3296-302
10. Barrett J W and Crane L 2000 A Lorentzian signature model for quantum general relativity Class. Quantum Grav. 17 3101-18
11. De Pietri R, Freidel L, Krasnov K and Rovelli C 2000 Barrett-Crane model from a Boulatov-Ooguri field theory over a homogeneous space Nucl. Phys. B 574 785-806
12. Perez A and Rovelli C 2001 A spin foam model without bubble divergences Nucl. Phys. B 599 255-82
13. Perez A and Rovelli C 2001 Spin foam model for Lorentzian general relativity Phys. Rev. D 63 041501
14. Baez J C 1998 Spin foam models Class. Quantum Grav. 15 1827-58
15. Baez J C and Barrett J W 1999 The quantum tetrahedron in 3 and 4 dimensions Adv. Theor. Math. Phys. 3 815-50
16. Reisenberger M P and Rovelli C 2001 Spacetime as a Feynman diagram: the connection formulation Class. Quantum Grav. 18 12-40
17. Reisenberger M P and Rovelli C 2000 Spin foams as Feynman diagrams Preprint gr-qc/0002083
18. Perez A 2001 Finiteness of a spinfoam model for Euclidean quantum general relativity Nucl. Phys. B 599 427-34
19. Crane L, Perez A and Rovelli C 2001 A finiteness proof for the Lorentzian state sum spin foam model for quantum general relativity Preprint gr-qc/0104057
20. Crane L, Perez A and Rovelli C 2001 Perturbative finiteness in spin-foam quantum gravity Phys. Rev. Lett. 87 181301
21. Ashtekar A 1991 Lectures on Non Perturbative Canonical Gravity (Singapore: Word Scientific)
22. Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244
23. Barbero J F 1995 Real Ashtekar variables for Lorentzian signature space times Phys. Rev. D 51 5507-10
24. Ashtekar A and Lewandowski J 1995 Projective techniques and functional integration J. Math. Phys. 36 2170
25. Reisenberger M 1994 World sheet formulations of gauge theories and gravity Preprint gr-qc/941235
26. Rovelli C and Smolin L 1995 Spin networks and quantum gravity Phys. Rev. D 53 5743
27. Baez J 1996 Spin network states in gauge theory Adv. Math. 117 253-72
28. Penrose R 1971 Quantum Theory and Beyond ed T Bastin (Cambridge: Cambridge University Press)
29. Kogut J B and Susskind L 1975 Hamiltonian formulation of Wilson's and lattice gauge theories Phys. Rev. D 11 395
30. Furmanski W and Kolawa A 1987 Yang-Mills vacuum: an attempt of lattice loop calculus Nucl. Phys. B 291 594
31. Smolin L 1997 The future of spin networks Preprint gr-qc/9702030
32. Zapata J A 1999 A combinatorial approach to quantum gauge theories and quantum gravity Preprint UMI-99-01167
33. Smolin L 1992 Recent developments in non perturbative quantum gravity Quantum Gravity and Cosmology, Proc. 1991 GIFT Int. Seminar on Theoretical Physics (Singapore: World Scientific) webpage hep-th/9202022
34. Rovelli C and Smolin L 1995 Discreteness of the area and volume in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum)
35. Rovelli C and Smolin L 1995 Discreteness of the area and volume in quantum gravity Nucl. Phys. B 442 593 Rovelli C and Smolin L 1995 Nucl. Phys. B 456 734 (erratum)
36. Ashtekar A and Lewandowski J 1997 Quantum theory of gravity: I. Area operators Class. Quantum Grav. 14 A55-A81
37. Immirzi G 1997 Real and complex connections for canonical gravity Class. Quantum Grav. 14 L177-81
38. Ashtekar A, Baez J C and Krasnov K 2000 Quantum geometry of isolated horizons and black hole entropy Adv. Theor. Math. Phys. 4 1-94
39. Loll R 1997 Simplifying the spectral analysis of the volume operator Nucl. Phys. B 500 405-20
40. Ashtekar A and Lewandowski J 1997 Quantum theory of gravity: II. Volume operators Preprint gr-qc/9711031
41. Thieman T 1996 Anomaly-free formulation of non perturbative, four dimensional Lorentzian quantum gravity Phys. Lett. B 380 257
42. Gaul M and Rovelli C 2001 A generalized Hamiltonian constraint operator in loop quantum gravity and its simplest Euclidean matrix elements Class. Quantum Grav. 18 1593-624
43. 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
44. Di Bartolo C, Gambini R, Griego J and Pullin J 2000 Consistent canonical quantization of general relativity in the space of Vassiliev knot invariants Phys. Rev. Lett. 84 2314-7
45. Halliwell J and Hartle J B 1991 Wave functions constructed from an invariant sum over histories satisfy constraints Phys. Rev. D 43 1170-94
46. Reisenberger M and Rovelli C 2002 Spacetime states and covariant quantum theory Phys. Rev. D 65 125016
47. Jacobson T and Smolin L 1988 Non perturbative quantum geometries Nucl. Phys. B 299 295
48. Smolin L and Rovelli C 1990 Loop space representation of quantum general relativity Nucl. Phys. B 331 80
49. Hartle J B and Hawking S W 1983 Wave function of the universe Phys. Rev. D 28 2960-75
50. Gibbons G W and Hawking S W 1993 Euclidean Quantum Gravity (Singapore: World Scientific) p 586
51. Crane L 1993 Categorical physics Preprint hep-th/9301061
52. Crane L 1993 Topological field theory as the key to quantum gravity Preprint hep-th/9308126
53. Crane L and Yetter D 1993 A categorical construction of 4-D topological quantum field theories Quantum Topology ed L Kaufmann and R Baadhio (Singapore: World Scientific)
54. Reisenberger M P and Rovelli C 1997 'Sum over surfaces' form of loop quantum gravity Phys. Rev. D 56 3490-508
55. Rovelli C 1999 The projector on physical states in loop quantum gravity Phys. Rev. D 59 104015
56. Thieman T 1998 Kinematical Hilbert spaces for fermionic and Higgs quantum field theories Class. Quantum Grav. 15 1487-512
57. Reisenberger M P 1997 A left-handed simplicial action for Euclidean general relativity Class. Quantum Grav. 14 1753-70
58. Reisenberger M P 1997 A lattice worldsheet sum for 4-d Euclidean general relativity Preprint gr-qc/9711052
59. Plebanski J F 1977 On the separation of Einsteinian substructures J. Math. Phys. 18 2511
60. Baez J C 2000 An introduction to spin foam models of quantum gravity and BF theory Lect. Notes Phys. 543 25-94
61. Freidel L 2000 A Ponzano-Regge model of Lorentzian 3-dimensional gravity Nucl. Phys. Proc. Suppl. 88 237-40
62. Iwasaki J 1995 A definition of the Ponzano-Regge quantum gravity model in terms of surfaces J. Math. Phys. 36 6288-98
63. Iwasaki J 1994 A reformulation of the Ponzano-Regge quantum gravity model in terms of surfaces Preprint gr-qc/9410010
64. Vilenkin N and Klimyk A U 1993 Representation of Lie Groups and Special Functions (Dordrecht: Kluwer)
65. Ponzano G and Regge T 1968 Semiclassical limit of Racah coefficients Spectroscopy and Group Theoretical Methods in Physics ed F Block et al (Amsterdam: North-Holland)
66. Freidel L and Louapre D 2002 Diffeomorphisms and spin foam models Preprint gr-qc/0212001
67. Turaev V G and Viro O Y 1992 Statesum invariants of 3-manifolds and quantum 6j-symbols Topology 31 865-902
68. Turaev V G 1994 Quantum Invariants of Knots and 3-Manifolds (Berlin: de Gruyter)
69. Kauffman L H and Lins S L 1994 Temperley-Lieb Recoupling Theory and Invariants of 3-Manifolds (Princeton, NJ: Princeton University Press)
70. Girelli F, Oeckl R and Perez A 2002 Spin foam diagrammatics and topological invariance Class. Quantum Grav. 19 1093-108
71. Zapata J A 2002 Continuum spin foam model for 3d gravity Preprint gr-qc/0205037
72. Freidel L and Krasnov K 1999 Spin foam models and the classical action principle Adv. Theor. Math. Phys. 2 1183-247
73. Iwasaki J 1999 A surface theoretic model of quantum gravity Preprint gr-qc/9903112
74. Iwasaki J 2000 A lattice quantum gravity model with surface-like excitations in 4-dimensional spacetime Preprint gr-qc/0006088
75. Barbieri A 1997 Quantum tetrahedra and simplicial spin networks Preprint gr-qc/9707010
76. Markopoulou F and Smolin L 1997 Causal evolution of spin networks Nucl. Phys. B 508 409-30
77. Markopoulou F 1997 Dual formulation of spin network evolution Preprint gr-qc/9704013
78. Markopoulou F and Smolin L 1998 Quantum geometry with intrinsic local causality Phys. Rev. D 58 084032
79. Gambini R and Pullin J 2001 A finite spin-foam-based theory of three and four dimensional quantum gravity Preprint gr-qc/0111089
80. Thiemann T 1998 QSD IV: 2 + 1 Euclidean quantum gravity as a model to test 3 + 1 Lorentzian quantum gravity Class. Quantum Grav. 15 1249-80
81. Capovilla R, Jacobson T and Dell J 1991 A pure spin connection formulation of gravity Class. Quantum Grav. 8 59-73
82. Capovilla R, Jacobson T and Dell J 1989 General relativity without the metric Phys. Rev. Lett. 63 2325
83. Freidel L and Livine E R 2002 Spin networks for non compact groups Preprint hep-th/0205268
84. Gambini R and Pullin J 2002 Canonical quantization of general relativity in discrete spacetimes Preprint gr-qc/0206055
85. Di Bartolo C, Gambini R and Pullin J 2002 Canonical quantization of constrained theories on discrete spacetime lattices Preprint gr-qc/0206055
86. Bojowald M and Perez A spin foam quantization and anomalies (in preparation)
87. Boulatov D 1992 A model of three-dimensional lattice gravity Mod. Phys. Lett. A 7 1629-46
88. Ooguri H 1992 Topological lattice models in four dimensions Mod. Phys. Lett. A 7 2799-810
89. Petronio C and De Pietri R 2000 Feynman diagrams of generalized matrix models and the associated manifolds in dimension 4 J. Math. Phys. 41 6671-88
90. Freidel L and Louapre D 2002 Non-perturbative summation over 3D discrete topologies Preprint hep-th/0211026
91. Livine R, Perez A and Rovelli C 2001 2d manifold-independent spinfoam theory Preprint gr-qc/0102051
92. Haag R 1996 Local Quantum Physics: Fields, Particles, Algebras (New York: Springer)
93. Perez A and Rovelli C 2001 Observables in quantum gravity Preprint gr-qc/0104034
94. Baez J C, Christensen J D, Halford T R and Tsang D C 2002 Spin foam models of Riemannian quantum gravity Preprint gr-qc/0202017
95. Markopoulou F 2002 Coarse graining in spin foam models Preprint gr-qc/0203036
96. Markopoulou F 2000 An algebraic approach to coarse graining Preprint hep-th/0006199
97. Kreimer D 1998 On the Hopf algebra structure of perturbative quantum field theories Adv. Theor. Math. Phys. 2 303-34
98. Kreimer D 1999 On overlapping divergences Commun. Math. Phys. 204 669
99. Oeckl R 2002 Renormalization of discrete models without background Preprint gr-qc/0212047
100. Perez A 2001 Spinfoam models for quantum gravity PhD Thesis University of Pittsburgh, Pittsburgh
101. Crane L, Kauffman L and Yetter D N 1997 State-sum invariants of 4-manifolds J. Knot Theor. Ramifications 6 177-234
102. De Pietri R and Freidel L 1999 so(4) Plebanski action and relativistic spin foam model Class. Quantum Grav. 16 2187-96
103. Reisenberger M P 1999 On relativistic spin network vertices J. Math. Phys. 40 2046-54
104. Barrett J W 1998 The classical evaluation of relativistic spin networks Adv. Theor. Math. Phys. 2 593-600
105. Major S A and Seifert M D 2002 Modelling space with an atom of quantum geometry Class. Quantum Grav. 19 2211-28
106. Crane L and Yetter D N 1994 On the classical limit of the balanced state sum Preprint gr-qc/9712087
107. Barrett J W and Williams R M 1999 The asymptotics of an amplitude for the 4-simplex Adv. Theor. Math. Phys. 3 209-15
108. Baez J C, Christensen J D and Egan G 2002 Asymptotics of 10j symbols Preprint gr-qc/0208010
109. Freidel L and Louapre D 2002 Asymptotics of 6j and 1Dj symbols Preprint hep-th/0209134
110. Barrett J W and Steele C M 2002 Asymptotics of relativistic spin networks Preprint gr-qc/0209023
111. Perez A and Rovelli C 2001 3 + 1 spinfoam model of quantum gravity with spacelike and timelike components Phys. Rev. D 64 064002
112. Baez J C and Christensen J D 2002 Positivity of spin foam amplitudes Class. Quantum Grav. 19 2291-306
113. Pfeiffer H 2002 Positivity of relativistic spin network evaluations Preprint gr-qc/0211106
114. Mikovic A 2001 Quantum field theory of spin networks Class. Quantum Grav. 18 2827-50
115. Wightman A S 1956 Quantum field theory in terms of vacuum expectation values Phys. Rev. 101 860
116. Wightman A S 1964 PCT, Spin Statistics and All That (New York: Benjamin-Cummings)
117. Oriti D and Williams R M 2001 Gluing 4-simplices: a derivation of the Barrett-Crane spin foam model for Euclidean quantum gravity Phys. Rev. D 63 024022
118. Gel'fand I M 1966 Generalized Functions vol 5 (New York: Academic)
119. Baez J C and Barrett J W 2001 Integrability for relativistic spin networks Class. Quantum Grav. 18 4683-700
120. Oriti D 2002 Boundary terms in the Barrett-Crane spin foam model and consistent gluing Phys. Lett. B 532 363-72
121. Pfeiffer H 2002 Dual variables and a connection picture for the Euclidean Barrett-Crane model Class. Quantum Grav. 19 1109-38 (Preprint gr-qc/0112002)
122. Christensen D, Daniel J and Egan G 2002 An efficient algorithm for the Riemannian 10j symbols Class. Quantum Grav. 19 1185-94
123. Smolin L 2002 Private communication
124. Alexandrov S 2002 Hilbert space structure of covariant loop quantum gravity Phys. Rev. D 66 024028
125. Alexandrov S 2002 Choice of connection in loop quantum gravity Phys. Rev. D 65 024011
126. Alexandrov S and Livine E R 2002 SU(2) loop quantum gravity seen from covariant theory Preprint gr-qc/0209105
127. Livine E R 2002 Projected spin networks for Lorentz connection: linking spin foams and loop gravity Class. Quantum Grav. 19 5525-42 (Preprint gr-qc/0207084)
128. Capovilla R, Montesinos M, Prieto V A and Rojas E 2001 BF gravity and the Immirzi parameter Class. Quantum Grav. 18 L49
129. Livine R E and Oriti D 2002 Barrett-Crane spin foam model from generalized Bf-type action for gravity Phys. Rev. D 65 044025
130. Livine R E 2001 Immirzi parameter in the Barrett-Crane Model Preprint gr-qc/0103081
131. Arnsdorf M 2002 Relating covariant and canonical approaches to triangulated models of quantum gravity Class. Quantum Grav. 19 1065-92
132. Freidel L and Louapre D 2002 Asymptotics of 6j and 10j symbols Preprint hep-th/0209134
133. Reisenberger M P 1998 Classical Euclidean general relativity from 'left-handed area = right-handed area' Preprint gr-qc/9804061
134. Noui K and Roche Ph 2002 Cosmological deformation of Lorentzian spin foam models Preprint gr-qc/0211109
135. Buffenoir E and Roche P 1999 Harmonic analysis on the quantum Lorentz group Commun. Math. Phys. 207 499-555
136. Oriti D and Pfeiffer H 2002 A spin foam model for pure gauge theory coupled to quantum gravity Preprint gr-qc/0207041
137. Mikovic A 2002 Spin foam models of matter coupled to gravity Class. Quantum Grav. 19 2335-54
138. Mikovic A 2002 Quantum field theory of open spin networks and new spin foam models Preprint gr-qc/0202026
139. Morales-Tecotl H A and Rovelli C 1995 Loop space representation of quantum fermions and gravity Nucl. Phys. B 451 325-61
140. Morales-Tecotl H A and Rovelli C 1994 Fermions in quantum gravity Phys. Rev. Lett. 72 3642-5
141. Baez J and Krasnov K 1998 Quantization of diffeomorphism-invariant theories with fermions J. Math. Phys. 39 1251-71
142. Crane L 2002 Hypergravity and categorical Feynmanology Preprint gr-qc/0004043
143. Crane L 2001 A new approach to the geometrization of matter Preprint gr-qc/0110060
144. Ambjorn J 2002 Simplicial Euclidean and Lorentzian quantum gravity Preprint gr-qc/0201028
145. Ambjorn J, Jurkiewicz J and Loll R 2000 A non perturbative Lorentzian path integral for gravity Phys. Rev. Lett. 85 924-7
146. Ambjorn J, Jurkiewicz J and Loll R 2002 3d Lorentzian, dynamically triangulated quantum gravity Nucl. Phys. Proc. Suppl. 106 980-2
147. Livine E R and Oriti D 2002 Implementing causality in the spin foam quantum geometry Preprint gr-qc/0210064
148. Pfeiffer H 2002 On the causal Barrett-Crane model: measure, coupling constant, Wick rotation, symmetries and observables Preprint gr-qc/0212049
149. Stachel J 1991 Einstein and quantum mechanics Conceptual Problems of Quantum Gravity ed A Ashtekar and J Stachel (Boston, MA: Birkhauser)