Casting loop quantum cosmology in the spin foam paradigm

Classical and Quantum Gravity

Volumn 27, Issue 13, 2010, Pages

  Ashtekar, Abhay ^a   Campiglia, Miguel ^a   Henderson, Adam ^a  

^a PENNSYLVANIA STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 77953105091     PISSN: 02649381     EISSN: 13616382     Source Type: Journal    
DOI: 10.1088/0264-9381/27/13/135020     Document Type: Article

References (64)

1. Ashtekar A, Campiglia M and Henderson A 2009 Loop quantum cosmology and spin foams Phys. Lett. B 681 347-52
2. Rovelli C 2009 Lecture at 2nd School and Workshop on Quantum Gravity and Quantum Geometry (Corfu, Sept. 2009)
3. Ashtekar A and Lewandowski J 2004 Background independent quantum gravity: a status report Class. Quantum Grav. 21 R53-R152
4. Rovelli C 2004 Quantum Gravity (Cambridge: Cambridge University Press)
5. Thiemann T 2007 Introduction to Modern Canonical Quantum General Relativity (Cambridge: Cambridge University Press)
6. Feynman R P 1948 Space-time approach to non-relativistic quantum mechanics Rev. Mod. Phys. 20 367-87
7. Reisenberger M P and Rovelli C 1997 Sum over surfaces form of loop quantum gravity Phys. Rev. D 56 3490-508
8. Ashtekar A 1986 New variables for classical and quantum gravity Phys. Rev. Lett. 57 2244-7
9. Ashtekar A 1987 A new Hamiltonian formulation of general relativity Phys. Rev. D 36 1587-603
10. Horowitz G T 1989 Exactly soluble diffeomorphism-invariant theories Commun. Math. Phys. 125 417-37
11. Baez J 2000 An introduction to spinfoam models of BF theory and quantum gravity Lect. Notes Phys. 543 25-94 (arXiv:gr-qc/9905087v1)
12. Barrett J W and Crane L 1998 Relativistic spin-networks and quantum gravity J. Math. Phys. 39 3296-302
13. Ponzano G and Regge T 1968 Semi-classical limit of Racah coefficients Spectroscopic and Group Theoretic Methods in Physics ed F Bloch et al (Amsterdam: North Holland)
14. Regge T 1961 General relativity without coordinates Nuovo Cimento 19 558-71
15. Williams R M 1986 Quantum Regge calculus in the Lorentzian domain and its space-time formulation Class. Quantum Grav. 3 853-69
16. Barrett J W 1987 The geometry of classical Regge calculus Class. Quantum Grav. 4 1565-76
17. Boulatov D 1992 A Model of three-dimensional lattice gravity Mod. Phys. Lett. A 7 1629-46
18. Oriti D 2006 The group field theory approach to quantum gravity arXiv:gr-qc/0607032
19. Oriti D and Tlas T 2008 A new class of group field theories for 1st order discrete quantum gravity Class. Quantum Grav. 25 085011
20. Perez A 2004 Introduction to loop quantum gravity and spin foams arXiv:gr-qc/0409061
21. Marolf D 1995 Refined algebraic quantization: systems with a single constraint arXiv:gr-qc/9508015
22. Ashtekar A, Bombelli L and Corichi A 2005 Semiclassical states for constrained systems Phys. Rev. D 72 025008
23. Ashtekar A, Lewandowski J, Marolf D, Mouro J and Thiemann T 1995 Quantization of diffeomorphism invariant theories of connections with local degrees of freedom J. Math. Phys. 36 6456-93
24. Baez J C, Christensen J D, Halford T R and Tsang D C 2002 Spin foam models of Riemannian quantum gravity Class. Quantum Grav. 19 4627-48
25. Alesci E and Rovelli C 2007 The complete LQG propagator: I. Difficulties with the Barrett-Crane vertex Phys. Rev. D 76 104012
26. Engle J, Pereira R and Rovelli C 2007 The loop quantum gravity vertex amplitude Phys. Rev. Lett. 99 161301
27. Freidel L and Krasnov K 2008 A new spin foam model for 4d gravity Class. Quantum Grav. 25 125018
28. Engle J, Livine E, Pereira R and Rovelli C 2008 LQG vertex with finite Immirzi parameter Nucl. Phys. B 799 136-49
29. Engle J and Pereira R 2008 Coherent states, constraint classes, and area operators in the new spin-foam models Class. Quantum Grav. 25 105010
30. Kamin's ki W, Kisielowski M and Lewandowski J 2009 Spin-foams for all loop quantum gravity arXiv:0909.0939
31. Kamin's ki W, Kisielowski M and Lewandowski J 2009 The EPRL intertwiners and corrected partition function arXiv:0912.0540
32. Hamber H W 2009 Quantum gravity on the lattice Gen. Rel. Grav. 41 817-76
33. Baez J C and Christensen J D 2002 Positivity of spin foam amplitudes Class. Quantum Grav. 19 2291-306
34. Conrady F and Freidel L 2008 On the semiclassical limit of 4d spin foam models Phys. Rev. D 78 104023
35. Barrett J W, Dowdall R J, Fairbairn W J, Gomes H and Hellmann F 2009 A summary of the asymptotic analysis for the EPRL amplitude arXiv:0909.1882
36. Barrett J W, Fairbairn W J and Hellmann F 2009 Quantum gravity asymptotics from the SU(2) 15j symbol arXiv:0912.4907
37. Ashtekar A, Pawlowski T and Singh P 2006 Quantum nature of the big bang Phys. Rev. Lett. 96 141301
38. Ashtekar A, Pawlowski T and Singh P 2006 Quantum nature of the big bang: an analytical and numerical investigation: I Phys. Rev. D 73 124038
39. Ashtekar A, Pawlowski T and Singh P 2006 Quantum nature of the big bang: improved dynamics Phys. Rev. D 74 084003
40. Ashtekar A, Pawlowski T, Singh P and Vandersloot K 2006 Loop quantum cosmology of k = 1 FRW models Phys. Rev. D 75 024035
41. Szulc L, Kamin's ki W and Lewandowski J 2006 Closed FRW model in loop quantum cosmology Class. Quantum Grav. 24 2621-35
42. Vandersloot K 2007 Loop quantum cosmology and the k = -1 RW model Phys. Rev. D 75 023523
43. Ashtekar A, Corichi A and Singh P 2008 Robustness of predictions of loop quantum cosmology Phys. Rev. D 77 024046
44. Bentivegna E and Pawlowski T 2008 Anti-de Sitter universe dynamics in LQC Phys. Rev. D 77 124025
45. Ashtekar A and Pawlowski T Loop quantum cosmology with a positive cosmological constant (in preparation)
46. Ashtekar A, Pawlowski T and Singh P Loop quantum cosmology in the pre-inflationary epoch (in preparation)
47. Ashtekar A and Wilson-Ewing E 2009 Loop quantum cosmology of Bianchi type I models Phys. Rev. D 79 083535
48. Ashtekar A and Edward-Wilson E 2009 Loop quantum cosmology of Binachi II models Phys. Rev. D 80 123532
49. Ashtekar A and Edward-Wilson E 2009 arXiv:0910.1278
50. Martin-Benito M, Garay L J and Marugan G A M 2008 Hybrid quantum Gowdy cosmology: combining loop and Fock quantizations Phys. Rev. D 78 083516
51. Brizuela D, Mena-Marugan G and Pawlowski T 2009 Big bounce and inhomogeneities arXiv:0902.0697
52. Mena-Marugan G and Martin-Benito M 2009 Hybrid quantum cosmology: combining loop and Fock quantization Intl. J. Mod. Phys. A 24 2820-38
53. Ashtekar A 2009 Loop quantum cosmology: an overview Gen. Rel. Grav. 41 707-41
54. Oriti D 2005 The Feynman propagator for spin foam quantum gravity Phys. Rev. Lett. 94 111301
55. Kaminski W and Lewandowski J 2008 The flat FRW model in LQC: the self-adjointness Class. Quantum Grav. 25 035001
56. Reed M and Simon B 1975 Methods of Modern Mathematical Physics: Vol II (New York: Academic) (section X.12)
57. Woodard R P 2008 Cosmology is not a renormalization group flow Phys. Rev. Lett. 101 081301
58. Campiglia M, Henderson A and Nelson W 2010 Vertex expansion for the Bianchi I model (IGC Pre-print)
59. Rovelli C and Vidotto F 2008 Stepping out of homogeneity in loop quantum cosmology Class. Quantum Grav. 25 225024
60. Bianchi E, Rovelli C and Vidotto F 2010 Towards spinfoam cosmology arXiv:1003:3483
61. Rovelli C and Vidotto F 2009 On the spinfoam expansion in cosmology arXiv:0911.3097
62. Martin-Benito M, Marugan G A M and Pawlowski T 2009 Physical evolution in loop quantum cosmology: the example of vacuum Bianchi I Phys. Rev. D 80 084038
63. Henderson A 2009 Path integral formulation of loop quantum cosmology International Loop Quantum Gravity Seminar (http://relativity.phys.lsu.edu/ ilqgs/henderson031709.pdf)
64. Husain V and Winkler O 2009 Particles, spin foams and the Hamiltonian path integral (personal communication to A Ashtekar)