Note on the semiclassical approximation in quantum gravity

Gilad Lifschytz, Samir D. Mathur, and Miguel Ortiz
Phys. Rev. D 53, 766 – Published 15 January 1996
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Abstract

We reexamine the semiclassical approximation to quantum gravity in the canonical formulation, focusing on the definition of a quasiclassical state for the gravitational field. It is shown that a state with classical correlations must be a superposition of states of the form eiS. In terms of a reduced phase space formalism, this type of state can be expresesd as a coherent superposition of eigenstates of operators that commute with the constraints and so correspond to constants of the motion. Contact is made with the usual semiclassical approximation by showing that a superposition of this kind can be approximated by a WKB state with an appropriately localized prefactor. A qualitative analysis is given of the effects of geometry fluctuations, and the possibility of a breakdown of the semiclassical approximation due to interference between neighboring classical trajectories is discussed. It is shown that a breakdown in the semiclassical approximation can be a coordinate-dependent phenomenon, as has beeen argued to be the case close to a black hole horizon. © 1996 The American Physical Society.

  • Received 19 December 1994

DOI:https://doi.org/10.1103/PhysRevD.53.766

©1996 American Physical Society

Authors & Affiliations

Gilad Lifschytz and Samir D. Mathur

  • Center for Theoretical Physics, Laboratory for Nuclear Science, Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139

Miguel Ortiz

  • Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155

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Issue

Vol. 53, Iss. 2 — 15 January 1996

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