Conditional symmetries and the quantization of Bianchi Type I vacuum cosmologies with and without cosmological constant

Classical and Quantum Gravity

Volumn 19, Issue 6, 2002, Pages 1013-1025

  Christodoulakis, T ^a   Gakis, T ^a   Papadopoulos, G O ^a  

^a UNIVERSITY OF ATHENS   (Greece)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0042382788     PISSN: 02649381     EISSN: None     Source Type: Journal    
DOI: 10.1088/0264-9381/19/6/301     Document Type: Article

References (44)

1. Goroff M H and Sagnoti H 1986 Nucl. Phys. B 266 709 't Hooft G 1974 Proc. 1978 Cargese Summer School ed M Levy, S Deser, G 't Hooft and M Veltman Ann. Inst. Henri Poincare 20 69
2. Goroff M H and Sagnoti H 1986 Nucl. Phys. B 266 709 't Hooft G 1974 Proc. 1978 Cargese Summer School ed M Levy, S Deser, G 't Hooft and M Veltman Ann. Inst. Henri Poincare 20 69
3. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
4. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
5. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
6. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
7. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
8. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
9. Christodoulakis T and Zaneli J 1986 Nuovo Cimento B 93 22 Christodoulakis T and Zaneli J 1987 Class. Quantum Grav. 4 851 Christodoulakis T and Korfiatis E 1991 Nuovo Cimento B 106 239 Ashtekar A 1986 Phys. Rev. Lett. 57 2224 Ashtekar A 1985 Phys. Rev. D 31 1777 Jacobson T and Smolin L 1988 Nucl. Phys. B 299 295 Rovelli C and Smolin L 1990 Nucl. Phys. B 331 80
10. Munoz Masque J and Valdes Morales A 1994 J. Phys. A: Math. Gen. 27 23
11. For a comprehensive list of references, see Halliwell J 1990 Int. J. Mod. Phys. A 5 2473-94
12. See for example Amsterdamski P 1985 Phys. Rev. D 31 3073 Hawking S W and Lutreli J C 1984 Phys. Lett. B 143 83 DelCampo S and Vilenkin A 1989 Phys. Lett. B 224 45
13. See for example Amsterdamski P 1985 Phys. Rev. D 31 3073 Hawking S W and Lutreli J C 1984 Phys. Lett. B 143 83 DelCampo S and Vilenkin A 1989 Phys. Lett. B 224 45
14. See for example Amsterdamski P 1985 Phys. Rev. D 31 3073 Hawking S W and Lutreli J C 1984 Phys. Lett. B 143 83 DelCampo S and Vilenkin A 1989 Phys. Lett. B 224 45
15. Christodoulakis T and Papadopoulos G O 2000 Preprint gr-qc/0009074 Christodoulakis T and Papadopoulos G O 2001 Phys. Lett. B 501 264-8 (Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Preprint gr-qc/0101103) Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Phys. Lett. B 514 149-54
16. Christodoulakis T and Papadopoulos G O 2000 Preprint gr-qc/0009074 Christodoulakis T and Papadopoulos G O 2001 Phys. Lett. B 501 264-8 (Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Preprint gr-qc/0101103) Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Phys. Lett. B 514 149-54
17. Christodoulakis T and Papadopoulos G O 2000 Preprint gr-qc/0009074 Christodoulakis T and Papadopoulos G O 2001 Phys. Lett. B 501 264-8 (Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Preprint gr-qc/0101103) Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Phys. Lett. B 514 149-54
18. Christodoulakis T and Papadopoulos G O 2000 Preprint gr-qc/0009074 Christodoulakis T and Papadopoulos G O 2001 Phys. Lett. B 501 264-8 (Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Preprint gr-qc/0101103) Christodoulakis T, Kofinas G and Papadopoulos G O 2001 Phys. Lett. B 514 149-54
19. Christodoulakis T, Korfiatis E and Papadopoulos G O 2001 Preprint gr-qc/0107050 (2001 Commun. Math. Phys. at press)
20. See e.g. Landau L D and Lifshitz E M 1986 The Classical Theory of Fields (Oxford: Pergamon) Tsamparlis M and Apostolopoulos P S 2000 J. Math. Phys. 41 7573
21. See e.g. Landau L D and Lifshitz E M 1986 The Classical Theory of Fields (Oxford: Pergamon) Tsamparlis M and Apostolopoulos P S 2000 J. Math. Phys. 41 7573
22. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
23. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
24. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
25. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
26. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
27. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
28. Ashtekar A and Samuel J 1991 Class. Quantum Grav. 8 2191 Folomeev V N and Gurovich V T 2000 Gravitation and Cosmology 6 19-26 Hervik S 2000 Class. Quantum Grav. 17 2765 (Hervik S 2000 Preprint gr-qc/0003084) Duncan M J and Jensen L G 1989 Nucl. Phys. B 312 662 Berger B K 1985 Phys. Rev. D 32 2485 Berger B K and Vogeli C N 1985 Phys. Rev. D 32 2477
29. Christodoulakis T, Kofinas G, Korfiatis E, Papadopoulos G O and Paschos A 2001 J. Math. Phys. 42 3580-608 (Christodoulakis T, Kofinas G, Korfiatis E, Papadopoulos G O and Paschos A 2000 Preprint gr-qc/0008050)
30. Christodoulakis T, Kofinas G, Korfiatis E, Papadopoulos G O and Paschos A 2001 J. Math. Phys. 42 3580-608 (Christodoulakis T, Kofinas G, Korfiatis E, Papadopoulos G O and Paschos A 2000 Preprint gr-qc/0008050)
31. Ellis G R F and MacCallum M A H 1969 Commun. Math. Phys. 12 108-41
32. Sneddon G E 1976 J. Phys. A: Math. Gen. 9 229 MacCallum M A H and Taub A H T 1972 Commun. Math. Phys. 25 173 Christodoulakis T and Korfiatis E 1994 Nuovo Cimento B 109 11
33. Sneddon G E 1976 J. Phys. A: Math. Gen. 9 229 MacCallum M A H and Taub A H T 1972 Commun. Math. Phys. 25 173 Christodoulakis T and Korfiatis E 1994 Nuovo Cimento B 109 11
34. Sneddon G E 1976 J. Phys. A: Math. Gen. 9 229 MacCallum M A H and Taub A H T 1972 Commun. Math. Phys. 25 173 Christodoulakis T and Korfiatis E 1994 Nuovo Cimento B 109 11
35. Dirac P A M 1950 Can. J. Math. 2 129 Dirac P A M 1958 Proc. R. Soc. A 246 333 Dirac P A M 1959 Phys. Rev. 114 924 Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University)
36. Dirac P A M 1950 Can. J. Math. 2 129 Dirac P A M 1958 Proc. R. Soc. A 246 333 Dirac P A M 1959 Phys. Rev. 114 924 Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University)
37. Dirac P A M 1950 Can. J. Math. 2 129 Dirac P A M 1958 Proc. R. Soc. A 246 333 Dirac P A M 1959 Phys. Rev. 114 924 Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University)
38. Dirac P A M 1950 Can. J. Math. 2 129 Dirac P A M 1958 Proc. R. Soc. A 246 333 Dirac P A M 1959 Phys. Rev. 114 924 Dirac P A M 1964 Lectures on Quantum Mechanics (New York: Belfer Graduate School of Science, Yeshiva University)
39. Kuchař K V and Hajiceck P 1990 Phys. Rev. D 41 1091 Kuchař K V and Hajiceck P 1990 J. Math. Phys. 31 1723
40. Kuchař K V and Hajiceck P 1990 Phys. Rev. D 411091 Kuchař K V and Hajiceck P 1990 J. Math. Phys. 31 1723
41. Kuchař K V 1982 J. Math. Phys. 23 1647-61
42. Harvey A 1979 J. Math. Phys. 20 251-8
43. Carabedian P R 1986 Partial Differential Equations (New York: Chelsea)
44. Henneaux M, Pilati M C and Teitelboim C 1982 Phys. Lett. B 110 123