Loop-quantum-gravity vertex amplitude

Physical Review Letters

Volumn 99, Issue 16, 2007, Pages

  Engle, Jonathan ^a   Pereira, Roberto ^a   Rovelli, Carlo ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

CONSTRAINT THEORY; COVARIANCE MATRIX; MATHEMATICAL MODELS; STATE SPACE METHODS;

BARRETT CRANE MODELS; LOOP QUANTUM GRAVITY; REGGE DISCRETIZATION; SPIN FOAM MODELS;

QUANTUM THEORY;

EID: 35348831786     PISSN: 00319007     EISSN: 10797114     Source Type: Journal    
DOI: 10.1103/PhysRevLett.99.161301     Document Type: Article

References (54)

1. A. Ashtekar, arXiv:gr-qc/0702030;
2. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity CQGRDG 0264-9381 21, R53-R152 (2004); 10.1088/0264-9381/21/11/003
3. T. Thiemann, Introduction to Modern Canonical Quantum General Relativity (Cambridge University Press, Cambridge, England, 2007).
4. C. Rovelli, Quantum Gravity (Cambridge University Press, Cambridge, England, 2004).
5. C. Rovelli and L. Smolin, Phys. Rev. Lett. 61, 1155 (1988); PRLTAO 0031-9007 10.1103/PhysRevLett.61.1155
6. C. Rovelli and L. Smolin, Nucl. Phys. NUPBBO 0550-3213 B331, 80 (1990); 10.1016/0550-3213(90)90019-A
7. A. Ashtekar, C. Rovelli, and L. Smolin, Phys. Rev. Lett. 69, 237 (1992); PRLTAO 0031-9007 10.1103/PhysRevLett.69.237
8. C. Rovelli and L. Smolin, Nucl. Phys. NUPBBO 0550-3213 B442, 593 (1995); 10.1016/0550-3213(95)00150-Q
9. C. Rovelli L. Smolin Nucl. Phys. NUPBBO 0550-3213 B456, 734 (1995);
10. A. Ashtekar and J. Lewandowski, Classical Quantum Gravity CQGRDG 0264-9381 14, A55 (1997); 10.1088/0264-9381/14/1A/006
11. A. Ashtekar J. Lewandowski Adv. Theor. Math. Phys. 1095-0761 1, 388 (1998).
12. T. Thiemann, Classical Quantum Gravity CQGRDG 0264-9381 15, 839 (1998); 10.1088/0264-9381/15/4/011
13. T. Thiemann Classical Quantum Gravity CQGRDG 0264-9381 23, 2249 (2006). 10.1088/0264-9381/23/7/003
14. A. Perez, Classical Quantum Gravity CQGRDG 0264-9381 20, R43 (2003); 10.1088/0264-9381/20/6/202
15. D. Oriti, Rep. Prog. Phys. RPPHAG 0034-4885 64, 1703 (2001). 10.1088/0034-4885/64/12/203
16. J.C. Baez, Lect. Notes Phys. LNPHA4 0075-8450 543, 25 (2000);
17. J.C. Baez Classical Quantum Gravity CQGRDG 0264-9381 15, 1827 (1998); 10.1088/0264-9381/15/7/004
18. M. Reisenberger and C. Rovelli, Classical Quantum Gravity CQGRDG 0264-9381 18, 121 (2001); 10.1088/0264-9381/18/1/308
19. M. Reisenberger and C. Rovelli, in Florence 2001, A Relativistic Spacetime Odyssey, edited by, I. Ciufolini, D. Dominici, and, L. Lusanna, (World Scientific, Singapore, 2003) p. 431.
20. M. Reisenberger, Classical Quantum Gravity CQGRDG 0264-9381 14, 1753 (1997); 10.1088/0264-9381/14/7/012
21. M. Reisenberger arXiv:gr-qc/9804061;
22. M. Reisenberger arXiv:gr-qc/9711052;
23. R. De Pietri and L. Freidel, Classical Quantum Gravity CQGRDG 0264-9381 16, 2187 (1999). 10.1088/0264-9381/16/7/303
24. G. Ponzano and T. Regge, in Spectroscopy and Group Theoretical Methods in Physics, edited by, F. Bloch, (North-Holland, Amsterdam, 1968).
25. C. Rovelli, Phys. Rev. D PRVDAQ 0556-2821 48, 2702 (1993). 10.1103/PhysRevD.48.2702
26. K. Noui and A. Perez, Classical Quantum Gravity CQGRDG 0264-9381 22, 1739 (2005). 10.1088/0264-9381/22/9/017
27. J.W. Barrett and L. Crane, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 39, 3296 (1998); 10.1063/1.532254
28. R. DePietri, L. Freidel, K. Krasnov, and C. Rovelli, Nucl. Phys. NUPBBO 0550-3213 B574, 785 (2000); 10.1016/S0550-3213(00)00005-5
29. A. Perez and C. Rovelli, Nucl. Phys. NUPBBO 0550-3213 B599, 255 (2001); 10.1016/S0550-3213(01)00030-X
30. D. Oriti and R.M. Williams, Phys. Rev. D PRVDAQ 0556-2821 63, 024022 (2000). 10.1103/PhysRevD.63.024022
31. A. Perez, Nucl. Phys. NUPBBO 0550-3213 B599, 427 (2001); 10.1016/S0550-3213(01)00014-1
32. L. Crane, A. Perez, and C. Rovelli, Phys. Rev. Lett. 87, 181301 (2001); PRLTAO 0031-9007 10.1103/PhysRevLett.87.181301
33. A. Perez and C. Rovelli, Phys. Rev. D PRVDAQ 0556-2821 63, 041501 (2001); 10.1103/PhysRevD.63.041501
34. L. Crane, A. Perez, and C. Rovelli, arXiv:gr-qc/0104057.
35. C. Rovelli, Phys. Rev. Lett. 97, 151301 (2006); PRLTAO 0031-9007 10.1103/PhysRevLett.97.151301
36. L. Modesto and C. Rovelli, Phys. Rev. Lett. 95, 191301 (2005); PRLTAO 0031-9007 10.1103/PhysRevLett.95.191301
37. E. Bianchi, L. Modesto, C. Rovelli, and S. Speziale Classical Quantum Gravity CQGRDG 0264-9381 23, 6989 (2006); 10.1088/0264-9381/23/23/024
38. S. Speziale, J. High Energy Phys. JHEPFG 1029-8479 05 (2006) 039; 10.1088/1126-6708/2006/05/039
39. E. Livine, S. Speziale, and J. Willis, Phys. Rev. D 75, 024038 (2007); PRVDAQ 0556-2821 10.1103/PhysRevD.75.024038
40. E.R. Livine and S. Speziale, J. High Energy Phys. JHEPFG 1029-8479 11 (2006) 092. 10.1088/1126-6708/2006/11/092
41. J.C. Baez, J.D. Christensen, T.R. Halford, and D.C. Tsang, Classical Quantum Gravity CQGRDG 0264-9381 19, 4627 (2002). 10.1088/0264-9381/19/18/301
42. E. Alesci and C. Rovelli, The Complete LQG Propagator I. Difficulties with the Barrett-Crane Vertex (to be published).
43. P.A.M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).
44. S. Alexandrov, Phys. Rev. D PRVDAQ 0556-2821 65, 024011 (2001); 10.1103/PhysRevD.65.024011
45. S. Alexandrov and E. Livine, Phys. Rev. D PRVDAQ 0556-2821 67, 044009 (2003); 10.1103/PhysRevD.67.044009
46. E. Buffenoir, M. Henneaux, K. Noui, and Ph. Roche, Classical Quantum Gravity CQGRDG 0264-9381 21, 5203 (2004); 10.1088/0264-9381/21/22/012
47. E.R. Livine and S. Speziale, arXiv:0705.0674.
48. L. Freidel, Int. J. Theor. Phys. IJTPBM 0020-7748 44, 1769 (2005). 10.1007/s10773-005-8894-1
49. M. Reisenberger, J. Math. Phys. (N.Y.) JMAPAQ 0022-2488 40, 2046 (1999). 10.1063/1.532850
50. A. Perez, Adv. Theor. Math. Phys. 1095-0761 5, 947 (2002);
51. A. Perez Adv. Theor. Math. Phys. 1095-0761 6, 593 (2003);
52. M. Reisenberger, arXiv:gr-qc/9711052;
53. L. Freidel and K. Krasnov, Adv. Theor. Math. Phys. 1095-0761 2, 1183 (1999).
54. J.C. Baez and J.W. Barrett, Adv. Theor. Math. Phys. 3, 815 (1999). 1095-0761