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Dimensional reduction and renormalizability of the Wheeler-DeWitt equation

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Il Nuovo Cimento B (1971-1996)

Summary

We solve the Wheeler-DeWitt equation for the wave function as an expansion in powers of the Planck mass. Expectation values computed with the leading-order approximation are reduced to the expectation value in three-dimensional Euclidean Einstein gravity theory. This means that «new phase» (the dynamical system described by the three-dimensional quantum Einstein gravity) exists at the region beyond the Planck scale. We also briefly discuss about the renormalizability of the Wheeler-DeWitt equation for (N+1)-dimensional Lorentzian manifolds (N>3).

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Authors and Affiliations

  1. Kibi Institute of Fundamental Research, 1384 Tujita, Mabi-cho, Kibi-gun, Okayama-ken, Japan

    T. Horiguchi

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  1. T. Horiguchi
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Horiguchi, T. Dimensional reduction and renormalizability of the Wheeler-DeWitt equation. Nuovo Cimento B 110, 839–856 (1995). https://doi.org/10.1007/BF02820152

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  • DOI: https://doi.org/10.1007/BF02820152

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