Reality Conditions in Nonperturbative Quantum Cosmology

Abstract

We carry out the nonperturbative canonical quantization of several types of cosmological models that have already been studied in the geometrodynamic formulation using the complex path-integral approach. We establish a relation between the choices of complex contours in the path integral and the sets of reality conditions for which the metric representation is well defined, proving that the ambiguity in the selection of complex contours disappears when one imposes suitable reality conditions. In most of the cases, the wave functions defined by means of the path integral turn out to be non-normalizable and cannot be accepted as proper quantum states. Moreover, the wave functions of the Universe picked out in quantum cosmology by the no-boundary condition and the tunneling proposals do not belong, in general, to the Hilbert space of quantum states. Finally, we show that different sets of reality conditions can lead to equivalent quantum theories. This fact enables us to extract physical predictions corresponding to Lorentzian gravity from quantum theories constructed with other than Lorentzian reality conditions.

34 pages, Preprint CGPG-93/9-3

References in corpus (3)

• Canonical Quantization of Spherically Symmetric Gravity in Ashtekar's Self-Dual Representation
• Unique determination of an inner product by adjointness relations in the algebra of quantum observables
• Non-Perturbative Canonical Quantization of Minisuperspace Models: Bianchi Types I and II

Cited by in corpus (9)

• An algebraic extension of Dirac quantization: Examples
• Canonical Quantization of the Gowdy Model
• Unstable no-boundary fluctuations from sums over regular metrics
• Is the Exponential of the Chern-Simons Action a Normalizable Physical State?
• Wormholes as Basis for the Hilbert Space in Lorentzian Gravity
• Correlations across horizons in quantum cosmology
• Bases of Wormholes in Quantum Cosmology
• CANONICAL QUANTIZATION OF CYLINDRICALLY SYMMETRIC MODELS
• Involutions on the Algebra of Physical Observables From Reality Conditions