Quantum geometry from 2+1 AdS quantum gravity on the torus
General Relativity and Quantum Cosmology
2011-02-23 v2 High Energy Physics - Theory
Mathematical Physics
math.MP
Abstract
Wilson observables for 2+1 quantum gravity with negative cosmological constant, when the spatial manifold is a torus, exhibit several novel features: signed area phases relate the observables assigned to homotopic loops, and their commutators describe loop intersections, with properties that are not yet fully understood. We describe progress in our study of this bracket, which can be interpreted as a q-deformed Goldman bracket, and provide a geometrical interpretation in terms of a quantum version of Pick's formula for the area of a polygon with integer vertices.
Cite
@article{arxiv.1006.0921,
title = {Quantum geometry from 2+1 AdS quantum gravity on the torus},
author = {J. E. Nelson and R. F. Picken},
journal= {arXiv preprint arXiv:1006.0921},
year = {2011}
}
Comments
19 pages, 11 figures, revised with more explanations, improved figures and extra figures. To appear GERG