Knots and Quantum Gravity: Progress and Prospects
Abstract
Recent work on the loop representation of quantum gravity has revealed previously unsuspected connections between knot theory and quantum gravity, or more generally, 3-dimensional topology and 4-dimensional generally covariant physics. We review how some of these relationships arise from a `ladder of field theories' including quantum gravity and BF theory in 4 dimensions, Chern-Simons theory in 3 dimensions, and the G/G gauged WZW model in 2 dimensions. We also describe the relation between link (or multiloop) invariants and generalized measures on the space of connections. In addition, we pose some research problems and describe some new results, including a proof (due to Sawin) that the Chern-Simons path integral is not given by a generalized measure.
Cite
@article{arxiv.gr-qc/9410018,
title = {Knots and Quantum Gravity: Progress and Prospects},
author = {John Baez},
journal= {arXiv preprint arXiv:gr-qc/9410018},
year = {2007}
}
Comments
22 pages in LaTeX