Radon transform of the Wheeler-De Witt equation and tomography of quantum states of the universe

General Relativity and Gravitation

Volumn 37, Issue 1, 2005, Pages 99-114

  Man'ko, V I ^a   Marmo, G ^a   Stornaiolo, C ^a  

^a UNIVERSITY OF NAPLES FEDERICO II   (Italy)

Author keywords

Quantum cosmology; Radon transformation; Wheeler De Witt equation

Indexed keywords

EID: 15244342298     PISSN: 00017701     EISSN: None     Source Type: Journal    
DOI: 10.1007/s10714-005-0005-3     Document Type: Article

References (41)

1. Radon, J.: Ber. Verh. Sächs. Acad. 69, 269 (1917)
2. von Neumann, J.: Mathematische Grundlagen der Quantenmechanik. Springer, Berlin (1932)
3. Landau, L.D., Physik, Z.: 45 430 (1927)
4. Wigner, E.: Phys. Rev. 40, 749 (1932)
5. Vogel, K., Risken, H.: Phys. Rev. A 40, 2847 (1989)
6. Smithey, D.T., Beck, M., Raymer, M. G., Faridani A.: Phys. Rev. Lett. 70, 1244 (1993)
7. Bertrand, J., Bertrand, D.: Found. Phys. 17, 397 (1987)
8. Mancini, S., Manko, V.I., Tombesi, P.: Quant. Semiclass. Opt. 7, 615 (1995)
9. Mancini, S., Manko, V.I., Tombesi, P.: Phys. Lett. A 213, 1, (1996)
10. Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Russ. Laser Res. 20, 421 (1999) Manko, V.I., Marmo, G., Sudarshan, B.C.G., Zaccaria, F.: Phys. Lett. A 273, 31 (2000) Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Phys. A: Math. Gen. 35, 7137 (2002)
11. Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Russ. Laser Res. 20, 421 (1999) Manko, V.I., Marmo, G., Sudarshan, B.C.G., Zaccaria, F.: Phys. Lett. A 273, 31 (2000) Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Phys. A: Math. Gen. 35, 7137 (2002)
12. Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Russ. Laser Res. 20, 421 (1999) Manko, V.I., Marmo, G., Sudarshan, B.C.G., Zaccaria, F.: Phys. Lett. A 273, 31 (2000) Manko, V.I., Marmo, G., Sudarshan, E.C.G., Zaccaria, F.: J. Phys. A: Math. Gen. 35, 7137 (2002)
13. Manko, O.V., Manko, V.I., Marmo, G.: Phys. Scr. 62, 446 (2000) Manko, O.V., Manko, V.I., Marmo, G.: J. Phys. A 35, 699 (2002)
14. Manko, O.V., Manko, V.I., Marmo, G.: Phys. Scr. 62, 446 (2000) Manko, O.V., Manko, V.I., Marmo, G.: J. Phys. A 35, 699 (2002)
15. Moyal, J.E.: Proc. Cambridge Philos. Soc. 45, 99 (1949)
16. Hawking, S.W.: Nucl. Phys. B 239, 257 (1984)
17. DeWitt, B.S.: Phys. Rev. 160, 1113 (1983) Wheeler, J.A.: In Battelle Rencontres. In DeWitt, C., Wheeler, J.A. (eds.) Benjamin, New York (1968)
18. DeWitt, B.S.: Phys. Rev. 160, 1113 (1983) Wheeler, J.A.: In Battelle Rencontres. In DeWitt, C., Wheeler, J.A. (eds.) Benjamin, New York (1968)
19. Hartle, J.B., Hawking, S.W.: Phys. Rev. D 28, 2960 (1983)
20. Hawking, S.W.: Intersection between Elementary Particle Physics and Cosmology. In Piran, T., Weinberg, S. (eds.) World Scientific, Singapore (1986)
21. Page, D.N.: Phys. Rev. D 34, 2267 (1986)
22. Halliwell, J.J.: Phys. Rev. D 38, 2468 (1988)
23. Rubakov, V.A.: Quantum cosmology [arXiv:gr-qc/9910025]
24. Parentani, R.: Phys. Rev. D 56, 4618 (1997)
25. Antonsen, F.: Deformation quantisation of Gravity [gr-qc/9712012]
26. Kodama, H.: Quantum cosmology in terms of the wigner function, KUCP-0014. Presented at 5th Marcel Grossmann Mtg., Perth, Western Australia, 8-12 Aug. 1988
27. Manko, V.I., Mendes, R.V.: Phys. Lett. A 263, 53 (1999)
28. Ashtekar, A.: Lectures on Non-perturbative Canonical Gravity. World Scientific, Singapore (1991) Ashtekar, A.: New Perspectives in Canonical Gravity. Bibliopolis, Napoli (1988)
29. Ashtekar, A.: Lectures on Non-perturbative Canonical Gravity. World Scientific, Singapore (1991) Ashtekar, A.: New Perspectives in Canonical Gravity. Bibliopolis, Napoli (1988)
30. Baez, J.C.: Diffeomorphism-invariant generalized measures on the space of connections modulo gauge transformations. In: Crane, L., Yetter, D. (eds.) Proceedings of the Conference on Quantum Topology, pp. 213-223. World Scientific, Singapore, 1994
31. Manko, V.I., Rosa, L., Vitale, P.: Phys. Lett B 439, 328 (1998)
32. Bajen, F., Flato, M., Fronsdal, M., Lichnerowicz, C., Sternheimer, D.: Lett. Math. Phys. 1, 521 (1975)
33. Manko, M.A.: J. Russ. Laser Res. 21, 421 (2000)
34. Manko, O.V., Manko, V.I.: J. Russ. Laser Res. 18, 407 (1997)
35. Manko, M.A.: J. Russ. Laser Res. 22, 168 (2001)
36. Louko, J.: Class. Quantum Grav. 4, 581 (1987)
37. Manko, V.I., Shchukin, E.V.: J. Russ. Laser Res. 22, 545 (2001)
38. Gousheh, S.S., Sepangi, H.R.: Phys. Lett. A 272, 304 (2000)
39. Basini, G., Capozziello, S., Longo, G.: Astron. Nach. 324, 275 (2003) Basini, G., Capozziello, S., Longo, G.: La Rivista del N. Cim. 25, N.11 (2002)
40. Basini, G., Capozziello, S., Longo, G.: Astron. Nach. 324, 275 (2003) Basini, G., Capozziello, S., Longo, G.: La Rivista del N. Cim. 25, N.11 (2002)
41. Manko, V.I., Mendes, R.V.: Physica D 145, 330 (2000)