Path integrals and instantons in quantum gravity: Minisuperspace models

Physical Review D - Particles, Fields, Gravitation and Cosmology

Volumn 53, Issue 12, 1996, Pages 6979-6990

  Marolf, Donald ^a  

^a UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0001567925     PISSN: 15507998     EISSN: 15502368     Source Type: Journal    
DOI: 10.1103/PhysRevD.53.6979     Document Type: Article

References (71)

1. G. W. Gibbons, in Fields and Geometry, Proceedings of the 22nd Karpacz Winter School of Theoretical Physics: Fields and Geometry, Karpacz, Poland, edited by A. Jadczyk (World Scientific, Singapore, 1986).
2. D. Garfinkle and A. Strominger, Phys. Lett. B 256, 146 (1992).
3. F. Dowker, J. Gauntlett, G. Gibbons and G. Horowitz, Phys. Rev. D 52, 6929 (1995);
4. F. Dowker, J. Gauntlett, S. Giddings and G. Horowitz, Phys. Rev. D 50, 2662 (1994).
5. E. Witten, Nucl. Phys. B195, 481 (1982).
6. S. W. Hawking, in Astrophysical Cosmology, edited by H. A. Brück et al., (Pontifica Academia Scientarium, Vatican City, 1982).
7. J. B. Hartle and S. W. Hawking, Phys. Rev. D 28, 2960 (1983);
8. S. W. Hawking, Nucl. Phys. B239, 257 (1984).
9. B. DeWitt, Phys. Rev. 160, 1113 (1967).
10. G. W. Gibbons, S. W. Hawking and M. J. Perry, Nucl. Phys. B138, 141 (1978).
11. S. B. Giddings, Int. J. Mod. Phys. A 5, 3811 (1989).
12. J. B. Hartle and K. Schleich, in Quantum Field Theory and Quantum Statistics, edited by T. A. Batalin et al., (Hilger, Bristol, 1987).
13. K. Schleich, Phys. Rev. D 39, 2192 (1989).
14. J. B. Hartle, J. Math. Phys. 30, 452 (1989).
15. J. J. Halliwell and J. B. Hartle, Phys. Rev. D 41, 1815 (1990).
16. J. J. Halliwell and J. Louko, Phys. Rev. D 39, 2206 (1989).
17. J. J. Halliwell and J. Louko, Phys. Rev. D 42, 3997 (1990).
18. N. P. Landsman, J. Geom. Phys. 15, 285 (1995).
19. D. Marolf, Class. Quantum. Grav. 12, 1199 (1994).
20. D. Marolf, Class. Quantum. Grav. 12, 1441 (1995).
21. A. Ashtekar, J. Lewandowski, D. Marolf, J. Mourão and T. Thiemann, J. Math. Phys. 36, 6456 (1995).
22. D. Marolf, in Proceedings of the Symposium on Differential Geometry and Mathematical Physics, edited by W. Kondracki (Banach Center Publications, Warsaw, in press).
23. A. Higuchi, Class. Quantum. Grav. 8, 1961 (1991);
24. A. Higuchi, Class. Quantum. Grav. 8, 1983 (1991);
25. A. Higuchi, Class. Quantum. Grav. 8, 2005 (1991);
26. A. Higuchi, Class. Quantum. Grav. 8, 2023 (1991).
27. M. Henneaux and C. Teitelboim, Ann. Phys. (N.Y.) 143, 127 (1982).
28. C. Misner, in Magic Without Magic, edited by J. R. Klauder (W.H. Freeman, San Francisco, 1972).
29. C. Misner, K. Thorne, and J. Wheeler, Gravitation (W. H. Freeman, New York, 1973), p. 805.
30. R. Jantzen, Commun. Math. Phys. 64, 211 (1979);
31. in Cosmology of the Early Universe, edited by L. Fang and R. Ruffini (World Scientific, Singapore, 1984).
32. M. Ryan and L. Shepley, Homogeneous Relativistic Cosmologies (Princeton University Press, Princeton, NJ, 1975).
33. A. Ashtekar, R. Tate and C. Uggla, Int. J. Mod. Phys. D 2, 15 (1993).
34. P. A. M. Dirac, Lectures on Quantum Mechanics (Yeshiva University, New York, 1964).
35. J. J. Halliwell, Phys. Rev. D 38, 2468 (1988).
36. P. Hájícek and K. Kuchar, Phys. Rev. D 41, 1091 (1990).
37. I. Moss, Ann. Inst. Henri Poincaré, 49, 341 (1988).
38. A. Ashtekar, Lectures on Non-Perturbative Canonical Gravity (World Scientific, Singapore, 1991).
39. A. Rendall, Class. Quantum Grav. 10, 605 (1993);
40. in Canonical Gravity: From Classical to Quantum, edited by J. Ehlers and H. Friedrichs (Springer, Berlin, 1994).
41. I. M. Gel’fand and N. Ya. Vilenkin, Generalized Functions, Vol. 4, Applications of Harmonic Analysis (Academic, New York, 1964).
42. J. Hartle and D. Marolf (in preparation).
43. D. Marolf, Class. Quantum. Grav. 12, 2469 (1995).
44. B. DeWitt, in Gravitation: An Introduction to Current Research, edited by L. Witten (Wiley, New York, 1962).
45. C. Rovelli, in Conceptual Problems of Quantum Gravity, edited by A. Ashtekar and J. Stachel (Birkhäuser, Boston, 1991), p. 141.
46. C. Rovelli, Phys. Rev. D 42, 2638 (1990).
47. C. Rovelli, Phys. Rev. D 43, 442 (1991).
48. C. Rovelli, Class. Quantum Grav. 8, 297 (1991).
49. J. B. Hartle, in Gravitation and Quantizations, Proceedings of the Les Houches Summer School, Les Houches, France, 1992, edited by J. Zinn-Justin and B. Julia, Les Houches Summer School Proceedings Vol. 57 (North-Holland, Amsterdam, 1995); Report No. gr-qc/9304006 (unpublished).
50. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems (Princeton University Press, Princeton, NJ, 1992), Sec. 15.1.
51. X. Lin and R. Wald, Phys. Rev. D 41, 244 (1990).
52. I. S. Gradshteyn and I. M. Ryzhik, Tables of Integrals, Series, and Products (Academic, New York, 1980).
53. D. N. Page, J. Math. Phys. 32, 3427 (1991).
54. A. Ashtekar and R. S. Tate, J. Math. Phys. 35, 6434 (1994).
55. J. Louko, Phys. Rev. D 48, 2708 (1993).
56. J. Louko and R. Laflamme, Phys. Rev. D 43, 2730 (1991).
57. C. Kiefer, Ann. Phys. (N.Y.) 207, 53 (1991).
58. R. F. Baierlein, D. H. Sharp and J. A. Wheeler, Phys. Rev. 126, 1864 (1962).
59. M. Henneaux, C. Teitelboim and J. D. Vergara, Nucl. Phys. B387, 391 (1992).
60. M. Henneaux and C. Teitelboim, Quantization of Gauge Systems [43], Sec. 1.4.
61. B. DeWitt, Rev. Mod. Phys. 29, 377 (1957).
62. K. Kuchar, J. Math. Phys. 24, 2122 (1983).
63. E. Baum, Phys. Lett. 133B, 183 (1983).
64. S. W. Hawking, Phys. Lett. 134B, 403 (1984).
65. S. Coleman, Nucl. Phys. B310, 643 (1988).
66. S. Giddings, in Modern Quantum Field Theory, Proceedings of the International Colloquium on Modern Field Theory, Tata Institute, Bombay, India, 1990, edited by S. Das et al., (World Scientific, Singapore, 1991).
67. J. Polchinski, Phys. Lett. B 219, 251 (1988).
68. A. Strominger, Nucl. Phys. B319, 722 (1989).
69. W. Fischler and I. Klebanov, Nucl Phys. B327, 157 (1989).
70. W. Fischler and L. Susskind, Phys. Lett. B 217, 48 (1989).
71. M. Duncan and L. Jensen, Nucl. Phys. B336, 100 (1990).