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arXiv · 1207.3759

Wheeler-DeWitt Equation in 2 + 1 Dimensions

Herbert W. Hamber·Reiko Toriumi·Ruth M. Williams
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Abstract

The infrared structure of quantum gravity is explored by solving a lattice version of the Wheeler-DeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wavefunction solutions is such that a finite correlation length emerges and naturally cuts off any infrared divergences. Properties of the lattice vacuum are consistent with the existence of an ultraviolet fixed point in $G$ located at the origin, thus precluding the existence of a weak coupling perturbative phase. The correlation length exponent is determined exactly and found to be $ν=6/11$. The results obtained so far lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class.

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Herbert W. Hamber, Reiko Toriumi, Ruth M. Williams. 2012-09-24. Wheeler-DeWitt Equation in 2 + 1 Dimensions. https://doi.org/10.1103/physrevd.86.084010

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