A proper-time cure for the conformal sickness in quantum gravity

Nuclear Physics B

Volumn 606, Issue 1-2, 2001, Pages 357-379

  Dasgupta, A ^a   Loll, R ^a  

^a ALBERT EINSTEIN INSTITUT   (Germany)

Author keywords

04.60. m; 04.60.Gw; 04.60.Kz; 04.60.Nc

Indexed keywords

EID: 0035833244     PISSN: 05503213     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0550-3213(01)00227-9     Document Type: Article

References (37)

1. Misner C.W. Feynman quantization of general relativity. Rev. Mod. Phys. 29:1957;497-509.
2. Leutwyler H. Gravitational field: equivalence of Feynman quantization and canonical quantization. Phys. Rev. 134:1964;B1155-1182.
3. Gibbons G.W., Hawking S.W., Perry M.J. Path integrals and the indefiniteness of the gravitational action. Nucl. Phys. B. 138:1978;141-150.
4. Hawking S.W. Hawking S.W., Israel W. General Relativity: an Einstein Centenary Survey. 1979;746-789 Cambridge Univ. Press, Cambridge.
5. Hartle J.B., Hawking S.W. Wave function of the universe. Phys. Rev. D. 28:1983;2960-2975.
6. Halliwell J.J., Louko J. Steepest descent contours in the path integral approach to quantum cosmology. The de Sitter minisuperspace model. Phys. Rev. D. 39:1989;2206-2215.
7. Halliwell J.J., Louko J. Steepest descent contours in the path integral approach to quantum cosmology. Microsuperspace. Phys. Rev. D. 40:1989;1868-1875.
8. Halliwell J.J., Louko J. Steepest descent contours in the path integral approach to quantum cosmology. A general method with applications to anisotropic minisuperspace models. Phys. Rev. D. 42:1990;3997-4031.
9. Halliwell J.J., Hartle J.B. Integration contours for the no-boundary wave function of the universe. Phys. Rev. D. 41:1990;1815-1834.
10. Schleich K. Conformal rotation in perturbative gravity. Phys. Rev. D. 36:1987;2342-2363.
11. Mazur P.O., Mottola E. The path integral measure, conformal factor problem and stability of the ground state of quantum gravity. Nucl. Phys. B. 341:1990;187-212.
12. Ambjørn J., Loll R. Non-perturbative Lorentzian quantum gravity, causality and topology change. Nucl. Phys. B. 536:1998;407-434 hep-th/9805108.
13. Ambjørn J., Jurkiewicz J., Loll R. A nonperturbative Lorentzian path integral for gravity. Phys. Rev. Lett. 85:2000;924-927 hep-th/0002050.
14. J. Ambjørn, J. Jurkiewicz, R. Loll, Dynamically triangulating Lorentzian quantum gravity, preprint Golm AEI-2001-049.
15. Ambjørn J., Jurkiewicz J., Loll R. Lorentzian and euclidean quantum gravity - analytical and numerical results. Thorlacius L., Jonsson T. M-Theory and Quantum Geometry. NATO Science Series. 2000;382-449 Kluwer Academic, hep-th/0001124.
16. Loll R. Discrete Lorentzian quantum gravity. Nucl. Phys. B Proc. Suppl. 94:2001;96-107 hep-th/0011194.
17. Regge T. General relativity without coordinates. Nuovo Cimento A. 19:1961;558-571.
18. Nakayama R. 2-d quantum gravity in the proper time gauge. Phys. Lett. B. 325:1994;347-353 hep-th/9312158.
19. Ambjørn J., Jurkiewicz J., Loll R. Non-perturbative 3d Lorentzian quantum gravity. preprint Golm AEI-2000-074 hep-th/0011276. to appear in Physical Review D.
20. Ambjørn J., Jurkiewicz J., Loll R. Computer simulations of 3d Lorentzian quantum gravity. Nucl. Phys. B Proc. Suppl. 94:2001;689-692 hep-lat/ 0011055.
21. Teitelboim C. Proper-time gauge in the quantum theory of gravitation. Phys. Rev. D. 28:1983;297-309.
22. Hawking S.W., Ellis G.F.R. The Large Scale Structure of Space-Time. 1973;Cambridge Univ. Press, Cambridge.
23. Fischer A.E. The theory of superspace. Carmeli M., et al. Relativity, Proc. of the Relativity Conf. in the Midwest. 1970;303-357 Plenum, New York.
24. Landau L.D., Lifshitz E.M. The Classical Theory of Fields. 4th rev. English edn. 1998;Butterworth-Heinemann, Oxford.
25. Faddeev L.D., Popov V.N. Covariant quantization of the gravitational field. Usp. Fiz. Nauk. 111:1973;427 Sov. Phys. Usp. 16:1974;777-788.
26. Faddeev L.D., Popov V.N. Covariant quantization of the gravitational field. Usp. Fiz. Nauk. 111:1973;427 Sov. Phys. Usp. 16:1974;777-788.
27. Bern Z., Blau S.K., Mottola E. General covariance of the path integral for quantum gravity. Phys. Rev. D. 43:1991;1212-1222.
28. Mottola E. Functional integration over geometries. J. Math. Phys. 36:1995;2470-2511.
29. DeWitt B. Quantum theory of gravity. The canonical theory. Phys. Rev. 160:1967;1113-1148.
30. Schoen R. Conformal deformation of a Riemannian metric to constant scalar curvature. J. Diff. Geom. 20:1984;479-495.
31. Distler J., Kawai H. Conformal field theory and 2D quantum gravity. Nucl. Phys. B. 321:1989;509-527.
32. Mazur P.O. Quantum gravitational measure for three-geometries. Phys. Lett. B. 262:1991;405-410.
33. Polyakov A.M. Quantum geometry of bosonic strings. Phys. Lett. B. 103:1981;207-210.
34. Carlip S. Quantum Gravity in 2+1 Dimensions. 1998;Cambridge Univ. Press, Cambridge.
35. Moncrief V. Reduction of the Einstein equation in 2+1 dimensions to a Hamiltonian system over Teichmüller space. J. Math. Phys. 30:1989;2907-2914.
36. Seriu M. Partition function for (2+1) -dimensional Einstein gravity. Phys. Rev. D. 55:1997;781-790.
37. S.W. Hawking, private communication to A.D.