The graviton vacuum as a distributional state in kinematic loop quantum gravity

Classical and Quantum Gravity

Volumn 22, Issue 7, 2005, Pages 1207-1237

  Varadarajan, Madhavan ^a,b  

^a RAMAN RESEARCH INSTITUTE   (India)

^b UNIVERSITY OF MUNICH   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 17044435453     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/22/7/002     Document Type: Article

References (40)

1. Ashtekar A, Rovelli C and Smolin L 1991 Phys. Rev. D 44 1740
2. Varadarajan M 2001 Phys. Rev. D 64 104003
3. Varadarajan M 2002 Phys. Rev. D 66 024017
4. Rovelli C 1991 Class. Quantum Grav. 8 1613
5. Gambini R and Pullin J (ed) 1996 Loops, Knots, Gauge Theories and Quantum Gravity (Camridge: Cambridge University Press)
6. Ashtekar A and Lewandowski J 1997 Class. Quantum Grav. 14 A55
7. Thiemann T and Winkler O 2001 Class. Quantum Grav. 18 2561 Thiemann T and Winkler O 2001 Class. Quantum Grav. 18 4629
8. Thiemann T and Winkler O 2001 Class. Quantum Grav. 18 2561 Thiemann T and Winkler O 2001 Class. Quantum Grav. 18 4629
9. Ashtekar A and Lewandowski J 2001 Class. Quantum Grav. 18 L117 Ashtekar A, Fairhurst S and Willis J 2003 Class. Quantum Grav. 20 1031
10. Ashtekar A and Lewandowski J 2001 Class. Quantum Grav. 18 L117 Ashtekar A, Fairhurst S and Willis J 2003 Class. Quantum Grav. 20 1031
11. Thiemann T 2002 Complexifier coherent states for general relativity Preprint gr-qc/0206037
12. Conrady F 2004 Free vacuum for loop quantum gravity Preprint gr-qc/0409036
13. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
14. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
15. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
16. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
17. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
18. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
19. Ashtekar A, Rovelli C and Smolin L 1992 Phys. Rev. Lett. 69 237 Zwegaard J 1993 Phys. Lett. B 300 217 Borissov R 1994 Phys. Rev. D 49 923 Grot N and Rovelli C 1997 Gen. Rel. Grav. 29 1039 Arnsdorf M 1999 Approximating connections in loop quantum gravity Preprint gr-qc/9910084 Corichi A and Reyes J M 2001 Int. J. Mod. Phys. D 10 325 Tsushima T 2002 The expectation value of the metric operator with respect to Gaussian weave state in loop quantum gravity Preprint gr-qc/0212117
20. Bombelli L 2000 Statistical geometry of random weave states Proc. 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (Rome) (Preprint gr-qc/0101080) Bombelli L, Corichi A and Winkler O 2004 Semiclassical quantum gravity: statistics of combinatorial riemanniang geometries Preprint gr-qc/0409006
21. Bombelli L 2000 Statistical geometry of random weave states Proc. 9th Marcel Grossmann Meeting on Recent Developments in Theoretical and Experimental General Relativity, Gravitation and Relativistic Field Theories (Rome) (Preprint gr-qc/0101080) Bombelli L, Corichi A and Winkler O 2004 Semiclassical quantum gravity: statistics of combinatorial riemanniang geometries Preprint gr-qc/0409006
22. Gambini R and Pullin J 1999 Phys. Rev. D D59 124021
23. Alfaro J, Morales-Tecotl H A and Urrutia L F 2000 Phys. Rev. Lett. 84 2318
24. Collins J, Perez A, Sudarsky D, Urrutia L and Vucetich H 2004 Phys. Rev. Lett. 93 191301
25. Iwasaki J and Rovelli C 1993 Int. J. Mod. Phys. D 1 533 Iwasaki J and Rovelli C 1994 Class. Quantum Grav. 11 1653
26. Iwasaki J and Rovelli C 1993 Int. J. Mod. Phys. D 1 533 Iwasaki J and Rovelli C 1994 Class. Quantum Grav. 11 1653
27. Zegwaard J 1993 Class. Quantum Grav. 10 S273
28. Fernando Barbero J 1995 Phys. Rev. D 51 5507
29. Ashtekar A and Lewandowski J 1995 J. Geom. Phys. 17 191
30. Marolf D and Mourão J 1995 Commun. Math. Phys. 583
31. Varadarajan M and Zapata J A 2000 Class. Quantum Grav. 17 4085
32. Sahlmann H, Thiemann T and Winkler O 2001 Nucl. Phys. B 606 401 Arnsdorf M and Gupta S 2000 Nucl. Phys. B 577 529
33. Sahlmann H, Thiemann T and Winkler O 2001 Nucl. Phys. B 606 401 Arnsdorf M and Gupta S 2000 Nucl. Phys. B 577 529
34. Yamasaki Y 1985 Measures on Infinite Dimensional Vector Spaces (Singapore: World Scientific)
35. Thiemann T 1998 Class. Quantum Grav. 15 839
36. Ashtekar A, Lewandowski J, Marolf D, Mourao J and Thiemann T 1995 J. Math. Phys. 36 6456
37. Kuchar K 1971 Phys. Rev. D 4 55
38. See, for example Lighthill M J 1975 Introduction to Fourier Analysis and Generalised Functions (Cambridge: Cambridge University Press) pp 69-70
39. Erdelyi A, Magnus W, Oberhettinger F and Tricomi F C (ed) 1954 Tables of Integral Transforms vol I (New York: McGraw-Hill)
40. Erdelyi A, Magnus W, Oberhettinger F and Tricomi F C (ed) 1954 Higher Transcendental Functions vol I (New York: McGraw-Hill)