Hilbert space structure of covariant loop quantum gravity

Physical Review D

Volumn 66, Issue 2, 2002, Pages

  Alexandrov, Sergei ^a,b,c  

^a CEA SACLAY   (France)

^b ECOLE NORMALE SUPÉRIEURE   (France)

^c ST PETERSBURG STATE UNIVERSITY   (Russian Federation)

Author keywords

[No Author keywords available]

Indexed keywords

ARTICLE; CALCULATION; GRAVITY; MATHEMATICAL ANALYSIS; PHYSICS; QUANTUM MECHANICS; SPACE;

EID: 0037101278     PISSN: 05562821     EISSN: None     Source Type: Journal    
DOI: 10.1103/PhysRevD.66.024028     Document Type: Article

References (37)

1. M. Gaul and C. Rovelli, Lectures given at the 35th Karpacz Winter School on Theoretical Physics: From Cosmology to Quantum Gravity, 1999, gr-qc/9910079.
2. G. Immirzi, Nucl. Phys. B (Proc. Suppl.) 57, 65 (1997).
3. C. Rovelli and T. Thiemann, Phys. Rev. D 57, 1009 (1998).
4. A. Ashtekar, J. Baez, A. Corichi, and K. Krasnov, Phys. Rev. Lett. 80, 904 (1998).
5. S. Alexandrov, Phys. Rev. D 65, 024011 (2002).
6. J. Samuel, Class. Quantum Grav. 17, L141 (2000);
7. Phys. Rev. D 63, 068501 (2001).
8. S. Alexandrov, Class. Quantum Grav. 17, 4255 (2000).
9. S. Alexandrov and D. Vassilevich, Phys. Rev. D 64, 044023 (2001).
10. C. Rovelli and L. Smolin, Nucl. Phys. B442, 593 (1995);
11. J. Lewandowski, "The operators of quantum gravity" lecture at the workshop on canonical and quantum gravity, Warsaw, 1995;
12. S. Frittelli, L. Lehner, and C. Rovelli, Class. Quantum Grav. 13, 2921 (1996).
13. A. Ashtekar and J. Lewandowski, Class. Quantum Grav. 14, A55 (1997).
14. A. Perez and C. Rovelli, Phys. Rev. D 63, 041501(R) (2001);
15. A. Perez and C. Rovelli, Phys. Rev. D 64, 064002 (2001).
16. A. O. Barut and R. Raczka, Theory of Group Representations and Applications (Polish Scientific Publishers, Warsaw, 1977).
17. A. Ashtekar and J. Lewandowskir, in Knots and Quantum Gravity, edited by J. Baez (Oxford University Press, Oxford, 1994);
18. J. Geom. Phys. 17, 191 (1995);
19. J. Math. Phys. 36, 2170 (1995).
20. J. F. Barbero, Phys. Rev. D 49, 6935 (1994);
21. J. F. Barbero, Phys. Rev. D 51, 5507 (1995);
22. J. F. Barbero, Phys. Rev. D 51, 5498 (1995);
23. J. F. Barbero, Phys. Rev. D 54, 1492 (1996).
24. S. Yu. Alexandrov and D. V. Vassilevich, Phys. Rev. D 58, 124029 (1998).
25. R. L. Anderson, R. Raczka, M. A. Rashid, and P. Winternitz, J. Math. Phys. 11, 1059 (1970).
26. W. Ruhl, The Lorentz Group and Harmonic Analysis (W.A. Benjamin Inc., New York, 1970).
27. M. A. Naimark, Am. Math. Soc. Trans. 36, 101 (1964).
28. D. Oriti, Rep. Prag. Phys. 64, 1489 (2001).
29. J. W. Barrett and L. Crane, Class. Quantum Grav. 17, 3101 (2000).
30. R. E. Livine and D. Oriti, Phys. Rev. D 65, 044025 (2002).
31. M. Bojowald, Class. Quantum Grav. 17,1489 (2000);
32. M. Bojowald, Class. Quantum Grav. 17, 1509 (2000);
33. M. Bojowald, Class. Quantum Grav. 18, 1055 (2001);
34. M. Bojowald, Class. Quantum Grav. 18, 1071 (2001).
35. T. Thiemann, Class. Quantum Grav. 15, 839 (1998);
36. T. Thiemann, Class. Quantum Grav. 15, 875 (1998).
37. I. M. Gel'fand, R. A. Minlos, and Z. Ya. Shapiro, Representations of the Rotation and Lorenlz Groups and Their Applications (Pergamon Press, New York, 1963), pp. 187-189.