1994/12/31 by Heinz-Dieter Conradi, Heinz - Dieter Conradi · 31 citations
Mathematics · Physics and Astronomy · #Boundary value problem #Classical mechanics #Cosmology #Cosmology and Gravitation Theories #Cylinder #Friedmann–Lemaître–Robertson–Walker metric #Function (biology) #Geometry #Mathematical analysis #Mathematical physics #Mathematics #Physics #Product (mathematics) #Quantum Electrodynamics and Casimir Effect #Quantum Mechanics and Applications #Quantum mechanics #Theoretical physics #WKB approximation #Wave function #gr-qc
paper · pdf · doi:10.1088/0264-9381/12/10/005
published in Classical and Quantum Gravity 12(10), 2423-2439 (IOP Publishing) · 21 pages, uses LaTeX2e, epsf.sty and float.sty, three figures (50 kb); changes: one figure added, new interpretation of quantizing procedure for the joined model and many minor changes
arxiv created 1995/07/13 · openalex publication_date 1995/10/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The Wheeler - DeWitt equation for a class of Kantowski - Sachs-like models is completely solved. The generalized models include the Kantowski - Sachs model with cosmological constant and pressureless dust. Likewise contained is a joined model which consists of a Kantowski - Sachs cylinder inserted between two FRW half-spheres. The (second-order) WKB approximation is exact for the wavefunctions of the complete set and this facilitates the product structure of the wavefunction for the joined model. In spite of the product structure the wavefunction cannot be interpreted as admitting no correlations between the different regions. This problem is due to the joining procedure and may therefore be present for all joined models. Finally, the symmetric initial condition for the wavefunction is analysed and compared with the `no-boundary' condition. The consequences of the different boundary conditions for the arrow of time are briefly mentioned.