Physics
Scientific paper
May 2000
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2000aps..nws.j2008p&link_type=abstract
American Physical Society, Second Meeting of the Northwest Section 2000 May 19-20, 2000 University of Oregon Eugene, Oregon, abs
Physics
Scientific paper
We examine the discrete Ponzano-Regge formulation of (2+1)-dimensional gravity in the context of a consistent histories approach to quantum cosmology. We consider the simplest 2-dimensional spatial boundaries of a 3-dimensional spacetime. The boundaries are described as the surface of a tetrahedral tessellation. Two classes of tessellation are considered. Using Ponzano-Regge wave functions, we calculate expectation values and uncertainties for these boundaries. In doing so, we observe finite size effects in the expectation values and uncertainties when the calculations fail to constrain the space of histories accessible to the system. Conversely, cutoff invariance is observed in our calculations provided the space of histories is constrained by an appropriate condition. It is thus suggested that physically meaningful results regarding the early state of our universe can be obtained providing we formulate the problem in a careful manner. A few of the difficulties inherent in quantum cosmology are thereby addressed in this study of an exactly calculable theory.
Petryk Roman
Schleich Kristin
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