- Access by Xinjiang University
Influence functional in two-dimensional dilaton gravity
Phys. Rev. D 58, 024009 – Published 22 June, 1998
DOI: https://doi.org/10.1103/PhysRevD.58.024009
Abstract
We evaluate the influence functional for two-dimensional models of dilaton gravity. This functional is exactly computed when conformal invariance is preserved, and it can be written as the difference between the Liouville actions on each closed-time-path branch plus a boundary term. From the influence action we derive the covariant form of the semiclassical field equations. We also study the quantum to classical transition in cosmological backgrounds. In the conformal case we show that the semiclassical approximation is not valid because there is no imaginary part in the influence action. Finally we show that the inclusion of the dilaton loop in the influence functional breaks conformal invariance and ensures the validity of the semiclassical approximation.
References (26)
- A. Strominger, in Les Houches Lectures on Black Holes, Talk given at NATO Advanced Study Institute: Les Houches Summer School, Les Houches, France, 1994, hep-th/9501071.
- C. G. Callan, S. B. Giddings, J. A. Harvey, and A. Strominger, Phys. Rev. D 45, 1005 (1992).
- J. G. Russo, L. Susskind, and L. Thorlacius, Phys. Rev. D 46, 344 (1992); ibid.47, 533 (1993).
- S. Bose, L. Parker, and Y. Peleg, Phys. Rev. D 54, 7490 (1996).
- J. P. Paz and S. Sinha, Phys. Rev. D 44, 1038 (1991).
- J. J. Halliwell, Phys. Rev. D 36, 3626 (1987).
- J. J. Halliwell, Phys. Rev. D 39, 2912 (1989).
- R. Lafamme and J. Louko, Phys. Rev. D 43, 3317 (1991).
- M. Gell-Mann and J. Hartle, in Complexity, Entropy and Physics on Information, edited by W. H. Zurek (Addison-Wesley, Reading, 1990); Phys. Rev. D 47, 3345 (1993); T. Brun, 47, 3383 (1993); H. F. Dowker and J. J. Halliwell, 46, 1580 (1992).
- R. Feynman and F. Vernon, Ann. Phys. (N.Y.) 24, 18 (1963).
- E. Calzetta and B. L. Hu, Phys. Rev. D 35, 495 (1987); ibid.R. D. Jordan, 33, 444 (1986); ibid.E. Calzetta and B. L. Hu, 40, 656 (1989).
- A. M. Polyakov, Phys. Lett. 103B, 207 (1981).
- E. Calzetta and B. L. Hu, Phys. Rev. D 49, 6636 (1994).
- F. C. Lombardo and F. D. Mazzitelli, Phys. Rev. D 53, 2001 (1996).
- E. Calzetta and F. D. Mazzitelli, Phys. Rev. D 42, 4066 (1990).
- F. Cooper, S. Habib, E. Mottola, J. P. Paz, and P. Anderson, Phys. Rev. D 50, 2848 (1994).
- F. C. Lombardo and F. D. Mazzitelli, Phys. Rev. D 55, 3889 (1997).
- C. G. Callan, S. B. Giddings, J. A. Harvey, and A. Strominger, Phys. Rev. D 45, 1005 (1992); ibid.S. Bose, L. Parker, and Y. Peleg, 54, 7490 (1996); Phys. Rev. Lett. 76, 861 (1996).
- S. M. Christensen and S. A. Fulling, Phys. Rev. D 15, 2088 (1977).
- B. S. DeWitt, in Relativity, Groups and Topology (Gordon and Breach, New York, 1964).
- N. D. Birrel and P. C. W. Davies, Quantum Fields in Curved Space (Cambridge University Press, Cambridge, 1982).
- F. D. Mazzitelli and J. G. Russo, Phys. Rev. D 47, 4490 (1993).
- E. Keski-Vakkuri, G. Lifschytz, S. D. Mathur, and M. E. Ortiz, Phys. Rev. D 51, 1764 (1995).
- A. Miković and V. Radovanović, Nucl. Phys. B504, 511 (1997); Class. Quantum Grav. 14, 2647 (1997); ibid.15, 827 (1998).
- G. A. Vilkovisky, in Quantum Theory of Gravity, edited by S. M. Christensen (Hilger, Bristol, 1984); A. O. Barvinsky and G. A. Vilkovisky, Nucl. Phys. B282, 163 (1987); ibid.B333, 471 (1990). I. G. Avramidi, Yad. Fiz. 49, 1185 (1989) [Sov. J. Nucl. Phys. 49, 735 (1989).
- S. Bose, L. Parker, and Y. Peleg, Phys. Rev. D 53, 7089 (1996).