WheelerDeWitt equation in 2+1 dimensions
Abstract
The infrared structure of quantum gravity is explored by solving a lattice version of the WheelerDeWitt equations. In the present paper only the case of 2+1 dimensions is considered. The nature of the wave function 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 fieldtheoretic universality class.
 Publication:

Physical Review D
 Pub Date:
 October 2012
 DOI:
 10.1103/PhysRevD.86.084010
 arXiv:
 arXiv:1207.3759
 Bibcode:
 2012PhRvD..86h4010H
 Keywords:

 04.60.m;
 04.60.Gw;
 04.60.Nc;
 98.80.Qc;
 Quantum gravity;
 Covariant and sumoverhistories quantization;
 Lattice and discrete methods;
 Quantum cosmology;
 High Energy Physics  Theory;
 General Relativity and Quantum Cosmology
 EPrint:
 56 pages, 7 figures, typos fixed, references added