Wheeler-DeWitt Equation in 2 + 1 Dimensions
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 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 . The results obtained so far lend support to the claim that the Lorentzian and Euclidean formulations belong to the same field-theoretic universality class.
Cite
@article{arxiv.1207.3759,
title = {Wheeler-DeWitt Equation in 2 + 1 Dimensions},
author = {Herbert W. Hamber and Reiko Toriumi and Ruth M. Williams},
journal= {arXiv preprint arXiv:1207.3759},
year = {2013}
}
Comments
56 pages, 7 figures, typos fixed, references added