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August 2015, Vol.359:80–96, doi:http://dx.doi.org/10.1016/j.aop.2015.04.016 [Broken]

Exact solutions of the Wheeler–DeWitt equation and the Yamabe construction

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- Eyo Eyo Ita III
- Chopin Soo

Abstract

Exact solutions of the Wheeler–DeWitt equation of the full theory of four dimensional gravity of Lorentzian signature are obtained. They are characterized by Schrödinger wavefunctionals having support on 3-metrics of constant spatial scalar curvature, and thus contain two full physical field degrees of freedom in accordance with the Yamabe construction. These solutions are moreover Gaussians of minimum uncertainty and they are naturally associated with a rigged Hilbert space. In addition, in the limit the regulator is removed, exact 3-dimensional diffeomorphism and local gauge invariance of the solutions are recovered.

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# Exact solutions of Wheeler–DeWitt & Yamabe Construction

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