Wigner distribution function and phase-space formulation of quantum cosmology

E. Calzetta and B. L. Hu
Phys. Rev. D 40, 380 – Published 15 July 1989
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Abstract

We present a phase-space formulation of quantum cosmology in terms of the Wigner distribution functions, which are useful for statistical descriptions of the quantum states of the Universe. Using a conformal formulation of field theory in curved space we derive a set of Wheeler-DeWitt-Vlasov equations and a generalized mass-shell condition satisfied by the Wigner functions up to the second adiabatic order. For minisuperspaces with diagonal metric and potentials of one variable, we find approximate solutions to these equations and exact solutions for the Bianchi type-II universe as an example. They all possess the correct classical limits.

  • Received 28 December 1988

DOI:https://doi.org/10.1103/PhysRevD.40.380

©1989 American Physical Society

Authors & Affiliations

E. Calzetta

  • Theoretical Physics Institute, Department of Physics, University of Alberta, Edmonton, Alberta, Canada T6G2J1

B. L. Hu

  • Department of Physics and Astronomy, University of Maryland, College Park, Maryland 20742 and Newman Laboratory of Nuclear Studies, Cornell University, Ithaca, New York 14853

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Vol. 40, Iss. 2 — 15 July 1989

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