Analysis of the Wheeler-DeWitt Equation beyond Planck Scale and Dimensional Reduction
T. Horiguchi, K. Maeda, M. Sakmaoto
Abstract
We solve the Wheeler-DeWitt equation for four-dimensional Einstein gravity as an expansion in powers of the Planck mass by means of a heat kernel regularization. Our results suggest that in the universe with a very small radius or with a very large curvature beyond a Planck scale expectation values of operators are reduced to calculations in a path integral representation of three-dimensional Einstein gravity.
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