1993/09/23 by Guillermo A. Mena Marugán, Guillermo A. Mena Marugan · 1 citation
Physics and Astronomy · #Ambiguity #Black Holes and Theoretical Physics #Canonical quantization #Classical mechanics #Cosmology and Gravitation Theories #Hilbert space #Loop quantum cosmology #Noncommutative and Quantum Gravity Theories #Path integral formulation #Physics #Quantization (signal processing) #Quantum #Quantum cosmology #Quantum gravity #Quantum mechanics #Theoretical physics #gr-qc
paper · pdf · doi:10.1088/0264-9381/11/3/012
published as Class.Quant.Grav.11:589-608,1994 · 34 pages, Preprint CGPG-93/9-3
arxiv created 1993/09/23 · openalex publication_date 1994/03/01 · arxiv updated 2010/04/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
We carry out the non-perturbative 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 wavefunctions defined by means of the path integral turn out to be non-normalizable and cannot be accepted as proper quantum states. Moreover, the wavefunctions 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.