Projector on physical states in loop quantum gravity

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 59, Issue 10, 1999, Pages

  Rovelli, Carlo ^a  

^a CENTRE DE PHYSIQUE THÉORIQUE   (France)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 85037893689     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.59.104015     Document Type: Article

References (56)

1. C. Rovelli and L. Smolin, Phys. Rev. Lett. 61, 1155 (1988);
2. C. RovelliL. SmolinNucl. Phys. B311, 80 (1990).
3. A. Ashtekar, Phys. Rev. Lett. 57, 2244 (1986);
4. A. AshtekarPhys. Rev. D 36, 1587 (1987).
5. For an introduction and complete references, see C. Rovelli, Living Rev. Relativ. 1, article 1 (1998).
6. C. Rovelli and L. Smolin, Nucl. Phys. B442, 593 (1995);
7. Nucl. Phys.C. RovelliL. SmolinB456, 734(E) (1995);
8. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997).
9. T. Thiemann, Phys. Lett. B 380, 257 (1996);
10. T. ThiemannClass. Quantum Grav. 15, 839 (1998).
11. M. Reisenberger and C. Rovelli, Phys. Rev. D 56, 3490 (1997).
12. F. Markopoulou and L. Smolin, Nucl. Phys. B508, 409 (1997);
13. F. MarkopoulouL. SmolinPhys. Rev. D 58, 084033 (1998).
14. J. Lewandowski and D. Marolf, Int. J. Mod. Phys. D 7, 299 (1998)
15. Int. J. Mod. Phys. DR. Gambini, J. Lewandowski, D. Marolf, and J. Pullin, 7, 97 (1998);
16. L. Smolin, “The classical limit and the form of the Hamiltonian constraint in nonperturbative quantum gravity,” gr-qc/9609034.
17. C. Rovelli, J. Math. Phys. 36, 6529 (1995).
18. J. Klauder, Ann. Phys. (N.Y.) 254, 419 (1997).
19. J. Govaerts, J. Phys. A 30, 603 (1997);
20. J. Govaerts and J. Klauder, “Solving gauge invariant systems without gauge fixing: the physical projector in 0+1 dimensional theories,” hep-th/9809119.
21. L.V. Prokhorov and S.V. Shabanov, Phys. Lett. B 216, 341 (1989);
22. L.V. ProkhorovS.V. ShabanovUsp. Fiz. Nauk 161, 13 (1991) [Sov. Phys. Usp. 34, 108 (1991)].
23. M. Henneaux and C. Teitelboim, Quantization of Constrained Systems (Princeton University Press, Princeton, NJ, 1992).
24. S.W. Hawking, in Relativity, Groups and Topology, Les Houches Session XL, Les Houches, France, 1983, edited by B. DeWitt and R. Stora (North-Holland, Amsterdam, 1984).
25. A. Ashtekar and J. Lewandowski, J. Math. Phys. 36, 2170 (1995);
26. J.C. Baez, Lett. Math. Phys. 31, 213 (1994).
27. T. Thiemann, Class. Quantum Grav. 15, 1487 (1998).
28. J. Baez, Class. Quantum Grav. 15, 1827 (1998).
29. M. Reisenberger, “Worldsheet formulations of gauge theories and gravity,” gr-qc/9412035.
30. J. Iwasaki, J. Math. Phys. 36, 6288 (1995).
31. J. Barret and L. Crane, J. Math. Phys. 39, 3296 (1998).
32. M. Reisenberger, Class. Quantum Grav. 14, 1753 (1997);
33. M. Reisenberger“A lattice worldsheet sum for 4-d Euclidean general relativity,” gr-qc/9711052.
34. M. Reisenberger, “Classical Euclidean general relativity from left-handed area = right-handed area,” gr-qc/9804061;
35. R. De Pietri and L. Freidel, “so(4) Plebanski action and relativistic spin foam model,” gr-qc/9804071.
36. For an overview of the present approaches to the problem of the description of quantum spacetime, see C. Rovelli/, in Gravitation and Relativity: At the turn of the Millenium, Proceedings of the GR15, Pune, India, 1997, edited by N. Dadhich and J. Narlikar (Inter-University Centre for Astronomy and Astrophysics, Pune, India, 1998), pp. 281–331, gr-qc/9803024.
37. C. Rovelli and P. Upadhya, “Loop quantum gravity and quanta of space: a primer,” gr-qc/9806079.
38. F. Barbero, Phys. Rev. D 49, 6935 (1994);
39. Phys. Rev. DF. Barbero51, 5507 (1995)
40. Phys. Rev. DF. Barbero51, 5498 (1995).
41. A. Ashtekar and C.J. Isham, Class. Quantum Grav. 9, 1433 (1992);
42. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão, and T. Thiemann, J. Math. Phys. 36, 6456 (1995).
43. R. DePietri and C. Rovelli, Phys. Rev. D 54, 2664 (1996);
44. R. DePietri, Class. Quantum Grav. 14, 53 (1997).
45. C. Rovelli and L. Smolin, Phys. Rev. D 52, 5743 (1995);
46. J.C. Baez, Adv. Math. 117, 253 (1996);in The Interface of Knots and Physics, edited by Kauffman (American Mathematical Society, Providence, RI, 1996), pp. 167–203.
47. R. Loll, Phys. Rev. Lett. 75, 3048 (1995);
48. A. Ashtekar and J. Lewandowski, Adv. Theor. Math. Phys 1, 388 (1998).
49. C.J. Isham, in Relativity, Groups and Topology II, Les Houches, France, 1983, edited by B. DeWitt and R. Stora (North-Holland, Amsterdam, 1984).
50. J.C. Baez and S. Sawin, J. Funct. Anal. 158, 253 (1998).
51. N.P. Landsman, Class. Quantum Grav. 12, L119 (1995).
52. C. Rovelli and L. Smolin, Phys. Rev. Lett. 72, 1994 (1946).
53. R. Borissov, R. DePietri, and C. Rovelli, Class. Quantum Grav. 14, 2793 (1997).
54. C. Rovelli, Class. Quantum Grav. 8, 297 (1991);
55. Class. Quantum Grav.C. Rovelli8, 317 (1991).
56. A. Barbieri, Nucl. Phys. B518, 714 (1998).